"Absence of evidence is not evidence of absence." - Bernard Heuvelmans, the father of cryptozoology, wrote that, and it's been quoted ever since. Is it valid?
I've dealt with this before, but I didn't resolve it. It's still pretty complicated.
Scientific answer: the validity of what I'll abbreviate as AEINEA depends on the circumstances.
Let's take the ivory-billed woodpecker. We know it existed. We know it hasn't been conclusively proven to exist in the U.S. since the Singer Tract in Louisiana was logged out in the 1950s. Some ornithologists came to accept its absence: others pointed out Southern woodlands were still relatively big and a few woodpeckers in a remote spot could be overlooked for a long time. So there was a split on whether AEINEA was valid.
Maybe this wasn't the best example, because there's still a split between the ornithologists who are sure they saw and videotaped it and those who have gone over the testimony and the tape and written them off as representing pileated woodpeckers. Still, the search was active for a very long time, and highly qualified experts took the AEINEA position. Some still do.
Anyone could have been forgiven for rejecting AEINEA in some cases, like the cahow or Bermuda petrel. It vanished for thee hundred years. No one was looking for it in 1906 when one was caught, killed, and stuffed - but misidentified. It wasn't until 1935 when one flew into a lighthouse window and the species' rediscovery began. If you'd been arguing the AEINEA position in 1934, you'd have been ridiculed.
Then we get to cryptozoology. To take the most topical subject, consider sasquatch. We have no hard evidence it existed or did exist. It's argued about whether it could exist in the purported habitat, but for the moment we'll accept Robert Pyle's well-argued book Where Bigfoot Walks and assume it could. (Pyle did not argue it did exist, only that it was possible).
You can still fly for hours over the Pacific Northwest and western Canada and not see a sign of human habitation. When sasquatch first made headlines in the 1950s (there are older stories, but let's start with the 1958 media explosion), it seemed logical to argue AEINEA, in part because no one had been looking for evidence.
In 2014, is it still valid?
A lot of people, include a very few scientists, do argue it. A small population of smart, wary animals, they say, can still avoid leaving good evidence. If we accept this as possible, the next question is, how long is AEINEA valid? If it was valid in 1958, it seems reasonable to accept it in 1968 and even 1978. 1988? 2000? 2014? (I am here setting aside the most intriguing evidence, the Patterson-Gimlin film, because it's still not definitive. We don't have a scrap of valid DNA, much less a definite piece of a specimen.)
If it's still good in 2014, how much longer? 2024? 2034? At some point, it will become indefensible. Skeptics have argued it's been indefensible for a long time. But even if it's valid now, it can't be valid forever.
Philip Klass once said UFO researchers lived under this curse: "You will never know more about UFOs than you do now." We don't know any more about sasquatch than we did 50 years ago. I personally leave the AEINEA door open just a crack because I know sincere people who are sure they've seen it. But I can't leave it open much longer.
Some cryptids are a bit different. The elongated marine animal known as the "sea serpent" has left no hard evidence anyone has collected for science, but it has the whole global ocean. It had better odds than sasquatch of not leaving hard evidence but still existing just because of that habitat. It does, however, become increasingly untenable that there is no evidence if the creature comes ashore to give birth. It's retreated, in essence: if there's a real animal, it's almost certainly pelagic. But I think AEINEA still has some validity here.
The "I think" part is tough. There is simply no way around some degree of subjectivity unless the habitat is entirely converted to asphalt or is so thoroughly known by humans that nothing could hide. This is where we are with Loch Ness, to my thinking.
The one thing we can say with certainty is that AEINEA cannot be valid forever for any large animal that lives on Earth. How long is it valid?
Assume for a moment sasquatch does NOT exist. If this is the case, there are sasquatch hunters who will come, in the coming decades, to decide AEINEA no longer applies. There are others who may die thinking it is still valid.
You'll notice that I really haven't come to a definite conclusion.
That's the thing.
YOU have to do that for each cryptid based on your own research and your own reason. I hope, in all cases, that AEINEA will turn out to be right. It won't, but I hope.