Saying a mammal is extinct is based on two criteria, it hasn't been seen for more than 50 years, or a massive search has come up empty.
Interestingly though, as many as a third of mammals thought to be extinct turn up again. University of Queensland scientists Diana Fisher and Simon Blomberg created a list of those 187 species that were listed as extinct since 1500, at least 67 of them turned up again.
Wired has a great piece on the scientists work:
Australia’s desert rat kangaroo, for example, was rediscovered in 1931 after having gone missing for almost a century, only to disappear again in 1935 when invasive red foxes moved into the area of the remaining survivors.
One thing to check, say the scientists, is how the species went extinct.
“If you think that a missing species is extinct and the main cause of decline was introduced predators such as feral foxes, cats or rats, then you are very likely to be right,” Fisher said. But, she added, “If the main cause of decline was habitat loss, you are quite likely to be wrong if you say that it’s extinct, unless it was restricted to a very small area.”
Fisher says that there are a couple species that have been listed as extinct that may be good candidates for a comeback.
...the Montane monkey-faced bat of the Solomon Islands, last seen on Guadalcanal in 1990, and Alcom’s pocket gopher, which was abundant in a high-elevation forest in Mexico in the late 1990’s but hasn’t been seen since.