It seems it was a mistake for the Ring to leave Isildur

[BalrogRingDestroyer]

A mistake anyway for the Ring and Sauron. Isildur was already the heir of Gondor and thus was a pretty powerful man. After it left him, it only came to lowly Hobbits (Deagol, Smeagol, Bilbo, Frodo, and Sam)). If it had stayed with Isildur, it could have corrupted him and started a civil war in Gondor and also, if he somehow held onto it without being deposed, been turned into a Wraith like the Nazgul and then just been made to give it to Sauron.

Even Elrond seems to hint at such, saying that perhaps death was a mercy to what fate COULD have befallen Isildur. Unlike the lowly Hobbits, even Smeagol for that matter, who was described as "not yet wholly ruined" despite possessing it for over 400 years, I think Isildur would have faded after 200 or so years and become a jerk and probably invaded Rohan and Arnor due to the corruption of the Ring. If Sauron had wanted a way to get rid of his enemies in the West, having the Ring go to Isildur would have been a great way of doing so. And of course, I can see Elrond and Celembrior tried to take the Ring from him and destroy it, it would have led to war between Men and Elves and, even if the Ring was destroyed in the end, would have led to a far more bittersweet Third Age than we got in the actual timeline.

 

[Squint-eyed Southerner]

We can only speculate, but there are some suggestive indications to be found in Unfinished Tales, "The Disaster of the Gladden fields". Describing the renewed attack by the Orcs on Isildur's force, we read that

[. . .] though it was unknown to them the Ring, cut from his black hand two years before, was still laden with l Sauron's evil will and called to all his servants for their aid.

So it seems the Ring itself was somehow "calling for rescue". Why or how that should be, two years after Sauron has "passed away", is a question. It could be that the Ring "thinks" he is still around somewhere, and perhaps he is, in spirit form, and returning to Mordor would allow him to reform sooner. But again, mere speculation.

We do know that Isildur had no desire or intention to wear it again; when his son Elendur asks if he can use its power to command the orcs, he responds

'I cannot use it. I dread the pain of touching it. And I have not yet found the strength to bend it to my will. It needs one greater than I now know myself to be. My pride has fallen. It should go to the keepers of the Three.'

If we want to attribute a kind of consciousness to the Ring, it would at this point be aware that gaining control of Isildur was unlikely; at any rate falling into the hands of the Elves must be avoided at all costs. On the other hand, volition could as easily be ascribed to Sauron's "evil will"; either is possible. It is, after all, still hot; when Isildur reluctantly decides to escape with it, "he set it upon his finger with a cry of pain".

And as usual with Tolkien, even the losing of it is made ambiguous:

There suddenly he knew that the Ring had gone. By chance, or chance well used, it had left his hand and gone where he could never hope to find it.

(Emphasis mine)

So it seems, however it happened, that a decision was made for the Ring to leave Isildur.

 

[Olorgando]

... Isildur was already the heir of Gondor and thus was a pretty powerful man. ... If it had stayed with Isildur, it could have corrupted him and started a civil war in Gondor ... I think Isildur would have faded after 200 or so years and become a jerk and probably invaded Rohan and Arnor due to the corruption of the Ring. ...

You seem to have the odd bit mixed up here.
Isildur took up the mantle of his Father Elendil, who was High King of the Númenóreans in exile in Middle-earth, and direct ruler of Arnor. Gondor had been founded by Isildur and Arnárion and was ruled by them jointly under their Father's High Kingship. Isildur had, after two years of instruction, left his nephew Meneldil as king of Gondor, while he was returning to Arnor (via Rivendell to pick up his only surviving son Valandil there), which was seat of the High Kingship established by Elendil, when he was attacked by Orcs and lost both the One Ring and his life in the River Anduin.

But this looks like a reason for the One Ring to abandon Isildur. Arnor was immensely further away from Mordor than Gondor. And it was flanked by the Grey Havens, now under Cirdan, and Rivendell under Elrond. Definitely a place much, much more difficult to reach from Mordor. And since what @Squint-eyed Southerner quoted above (from "The Disaster of the Gladden Fields" in Unfinished Tales) seems to indicate that Isildur had no wish to use the One Ring anymore, but rather give it to the Keepers of the Three, this would have been an even worse prospect for the One Ring.
Now from "The Council of Elrond" we know that the One Ring was dangerous even for these three, by then Cirdan, Elrond and Galadriel. But at the very beginning of the Third Age, and never mind Elrond's babble 3,000 years later, what was to stop Cirdan sending a special ship to Valinor, to have the One Ring handed over to Aulë for immediate destruction, something Aulë could have done with ease?

External to the legendarium, all of these explanatory writings post-date publication of LoTR. All of JRRT's "rationalizations" had to fit this historical fact. "What if" speculations (or fanfics) can be fun ...

 

[Goldilocks Gamgee]

Isildur had no wish to use the One Ring anymore, but rather give it to the Keepers of the Three,

I have a question.

He could he really have done it, parting willingly with the One Ring? He failed to do so at Mt. Doom, and I'm pretty sure the Ring's influence could only have grown on him since that time. Also, judging by the fact that he kept it with him always, it was hard for Isildur to let it out of sight. Obviously, the Ring was beginning to take control -- just a little further, and he could've been corrupted into a wraith.

 

[Olorgando]

I have a question.

He could he really have done it, parting willingly with the One Ring? He failed to do so at Mt. Doom, and I'm pretty sure the Ring's influence could only have grown on him since that time. Also, judging by the fact that he kept it with him always, it was hard for Isildur to let it out of sight. Obviously, the Ring was beginning to take control -- just a little further, and he could've been corrupted into a wraith.

Very valid point, reinforced by Gandalf quoting from Isildur's scroll, that he had found in the archives of Gondor, at the Council of Elrond.
A speculation of how he might have been able to might be that after the beyond-all-hope defeat (and disembodiment) of Sauron just earlier, the danger of the One Ring for corruption was not quite clear yet - most probably thought Sauron had been destroyed, not just (once more) disembodied. And the concept of a "weregild", strange as it may seem to us, may have been fairly common in the Iceland of the Eddas. A further speculation might go in the direction that Isildur took the One Ring from Sauron's hand, or rather severed finger, when it must have been blazing hot. When Isildur wrote that scroll in Minas Tirith, likely at least a couple of weeks later at the least (think of how long the diversionary force led by Aragorn took to reach the Black Gate, and it was still miles to Mount Doom), the writing was still faintly visible. Besides the heat, the emanation of evil (the One Ring had still to "learn" to disguise its purposes) could also have been repellent to anyone but Sauron. While Isildur's writing of the scroll quoted by Gandalf (earlier) and his statement in "Disaster of the Gladden Fields" (later) might be hard to reconcile, he had possession of the One ring for about two years at his death. Bilbo, after possessing it for 60 years, did give it up, if grudgingly and with some none-too-gentle prodding by Gandalf. As a human in a position of power, it is true, he may have been far more susceptible to the One Ring's temptations than the five Hobbits who followed him as Ring-bearer. But as one born in Númenor, of direct descent from Elros, he may have among humans (one of) the most resistant, too.

 

[Goldilocks Gamgee]

But how does it make sense for a place of birth to affect your susceptibility to evil? I get how descent and race could make a difference, but surely Isildur could not have been that different from Boromir, who was corrupted without ever being in control of the Ring, or Aragorn, who even deemed himself unable?

 

[Olorgando]

But how does it make sense for a place of birth to affect your susceptibility to evil? I get how descent and race could make a difference, but surely Isildur could not have been that different from Boromir, who was corrupted without ever being in control of the Ring, or Aragorn, who even deemed himself unable?

Well, places (Valinor, Tol Eressëa, Lothlórien - and Númenor) can be special in JRRT's Arda, but I guess it't better not to press this point too hard.

But Isildur was of direct descent from Elros, if not in the male line. But Elros's great-great-granddaughter Silmarien was the oldest child of Tar-Elendil, the fourth king of Númenor.

Then, Isildur was of the minority party of the Faithful in Númenor. As per HoMe vol 12 PoMe chapter VII "The Heirs of Elendil", Elendil lived 322 years, falling in that combat with Sauron together with Gil-galad. The last ruler of Númenor to pass 300 years (309) was the 18th one, Tar-Calmacil (SA 2516-2825). And Elendil most likely would have had some decades left if he hadn't fallen in battle. Same for Isildur, who was 234 when he fell in that Orc attack. Isildur's son Valandil reached 260, the next two rulers at least 250. That's Old Dwarf territory!

As to Aragorn, he was 39 generations after Isildur (born 2,929 years after Isildur's death). That's a big difference. He did have the sense to refuse the One Ring.
Boromir is an entirely different case altogether, even to Aragorn. As the heir apparent to the position of Steward of Gondor, he wasn't even of the royal line. And many people thought that he was more of a "middle man", closer to the Rohirrim in many ways in contrast to his father Denethor and brother Faramir. Boromir was something of a one-skill person, a warrior, and thus viewed the One Ring as a weapon to be used - which would have had disastrous consequences no matter which scenario one imagines.