That question stroke me this morning. Veganism is about not making decisions affecting non-human animal lives. Letting them live, and trying not to hurt them as much as possible.
Planète Vegan, the vegan bible for French-speaking people (it seems that it hat not been translated yet), says that veganism position about living with pets is not definitive and that adopting animals from shelters and letting them live in an environment as close as possible to their natural habitat may be compatible with veganism.
However, what happens when one of those animals you've rescued gets terribly sick and their days appear to be numbered? If we truly believe that they're going to die, should we stick to the principle that we have no right to rule their lives and let death happen? Or should we alleviate their suffering and take them to the vet and make them get euthanasia?
Disclaimer: don't worry, none of my rescued animals is in pain right now :)