Would preserving an otherwise-doomed animal in captivity (perhaps through cloning) be a way to sort of "make it up" to Mother Nature?
Make it up to her? She's the one that doomed them in the first place.
The other responders have mentioned the value of conservation for human benefit, but, what about nature's benefit?
For all the damage we've done with invasive exotic species, I think it'd be best for us to let nature handle her own benefits rather than us trying to help and end up fucking it up anyways.
But, trade-offs aside, if an animal is clearly doomed (or if we have already killed it off), and there is no way to feasibly return it to the wild, is it morally warranted for us to preserve a few specimens?
Meh. Its amoral.
If the "right" thing to do is to preserve nature's sovereignty over itself, it seems we've already failed.
If you presume that we are a part of nature, then whatever failures we have are nature's too.