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From their perspective, giving them up would have the same effect as destroying them, and that's something they're not willing to do except in the face of greater need, as Elrond and Glorfindel say:

There's no sensible reason for the Elves to provide mortals with a means of extending their lives, because to the Elves that's the worst thing you can do as a mortal.

It's worth emphasizing (as Avner Shahar-Kashtan points out in comments) that, at least as far as the Rings are concerned, this is what the Elves mean by "resisting the weariness of time"¹: they want to preserve the glory and beauty of their great works, but Middle-earth is stubbornly insistent in getting on with things.

From their perspective, giving them up would have the same effect as destroying them, and that's something they're not willing to do except in the face of greater need, as Elrond and Glorfindel say:

There's no sensible reason for the Elves to provide mortals with a means of extending their lives, because to the Elves that's the worst thing you can do as a mortal.

¹ That isn't to say that the Elves don't get personally weary from time; in Middle-earth they do, but largely because, as Wad Cheber points out in a comment on the question, they watch the cycles of the world go on while they themselves remain unchanged. Ultimately this is why (some of) the Elves yearn for Aman, where there is no natural decay. But the Rings aren't meant to resist that sort of personal weariness, except as a side-effect of preserving the other things the Elves value.

^{_{The Silmarillion IV OF the Rings of Power and the Third Age}}

^{_{The Silmarillion IV OF the Rings of Power and the Third Age}}

Because of the natural resiliency of the Elves, he was unable to acquire them in the Second Age. If they were given to Men, however, Sauron would have no such problems; the new, mortal bearers would fall under his dominion just as the Nine did, and then Sauron would have the Three Rings and be the stronger for it. This is considered "non-optimal" by the Elves, who rather want Sauron to keep his grubby mitts off their things.

^{_{The Silmarillion V OF the Rings of Power and the Third Age}}

^{_{The Silmarillion V OF the Rings of Power and the Third Age}}

Because of the natural resiliency of the Elves, he was unable to acquire them in the Second Age. If they were given to Men, however, Sauron would have no such problems; the new, mortal bearers would fall under his dominion just as the Nine did, and then Sauron would have the Three Rings and be the stronger for it. This is considered "non-optimal" by the Elves, who rather want Sauron to keep his grubby mitts off their things.

3. The Elves don't view the mortal fate as a bad thing. This is an idea that's a little tricky for us, limited mortal readers as we are, but in Tolkien's world death is a good thing. At least it seems like it to the immortals; one particular passage in The Silmarillion goes:

But the sons of Men die indeed, and leave the world; wherefore they are called the Guests, or the Strangers. Death is their fate, the gift of Ilúvatar, which as Time wears even the Powers [Valar and Maiar] shall envy.

^{_{The Silmarillion III Quenta Silmarillion Chapter 1: "Of the Beginning of Days"}}

A much-later conversation, between the Elves of Eressëa and the Men of Númenor, further indicates just how much of a gift the Elves view death:

The Eldar, you say, are unpunished, and even those who rebelled do not die. Yet that is to them neither reward nor punishment, but the fulfilment of their being. They cannot escape, and are bound to this world, never to leave it for so long as it lasts, for its life is there. And you are punished for the rebellion of Men, you say, in which you had small part, and so it is that you die. But that was not at first appointed for a punishment. Thus you escape, and leave the world, and are not bound to it, in hope or in weariness. Which of us therefore should envy the others?

^{_{The Silmarillion IV Akallabêth}}

There's no sensible reason for the Elves to provide mortals with a means of extending their lives, because to the Elves that's the worst thing you can do as a mortal.

1. When Sauron was presumed destroyed, the Elves were using them. It's worth remembering why the Elves wanted the Three Rings in the first place:

It was in Eregion that the counsels of Sauron [disguised as Annatar] were most gladly received, for in that land the Noldor desired ever to increase the skill and subtlety of their works. **Moreover they were not at peace in their hearts, since they had refused to return into the West, and they desired both to stay in Middle-earth, which indeed they loved, and yet to enjoy the bliss of those that had departed.

2. In the event of Sauron's return, he would use mortals to acquire the Three. This reason is more mercenary; Sauron really wanted the Three:

Because of the natural resiliency of the Elves, he was unable to acquire them in the Second Age. If they were given to Men, however, Sauron would have no such problems; they would fall under his dominion just as the Nine did, and then Sauron would have the Three Rings and be the stronger for it.

1. When Sauron was presumed destroyed, the Elves were using them. It's worth remembering why the Elves wanted the Three Rings in the first place (emphasis mine):

It was in Eregion that the counsels of Sauron [disguised as Annatar] were most gladly received, for in that land the Noldor desired ever to increase the skill and subtlety of their works. Moreover they were not at peace in their hearts, since they had refused to return into the West, and they desired both to stay in Middle-earth, which indeed they loved, and yet to enjoy the bliss of those that had departed.

2. In the event of Sauron's return, he would use mortals to acquire the Three. This reason is less mercenary; Sauron really wanted the Three:

Because of the natural resiliency of the Elves, he was unable to acquire them in the Second Age. If they were given to Men, however, Sauron would have no such problems; the new, mortal bearers would fall under his dominion just as the Nine did, and then Sauron would have the Three Rings and be the stronger for it. This is considered "non-optimal" by the Elves, who rather want Sauron to keep his grubby mitts off their things.