It seems like it would be very hard to determine if a creature has gone truly extinct.. to know if an animal is extinct you would have to be in all places at once. We've thought tons of animals have gone extinct millions of years ago yet out of nowhere they turn up in abundance. Not saying it's bad to watch over animals and ensure their survival, I'm just curious as how they declare these things.. wild animals tend to avoid humans in nature as it is anyways so just because you can't find it atm doesn't mean they're all dead.
We know a lot more about [most of] the species that still exist or have still existed within recent memory. Folks dedicate their entire scientific careers to specific endangered animals. They track and chart their decline, they know exactly where they live, eat, and breed. There comes a day when those folks can safely say something is extinct. Sure, it might be hard to say if there are no single, surviving hold out specimens of a certain species, but what's really important is if the overall breeding population has reached too small of a size to maintain itself, then the rest is just an inevitability. There is more assumption and less hard data for specimens from the fossil record in regard to extinction, so we end up with some pleasant surprises from mother nature once in awhile. Edit; Same general idea applies to plant life as well.