It's said to be a logical fallacy to consider absence of evidence, evidence of absence. But since it's impossible to find proof that A is nonexistent, under certain circumstances we can consider a lack of evidence, evidence that proves A does not exist. But is it enough?
What I think this idea is based on, is Occam's razor. Meaning because for A to be existent, one has to consider unnecessary assumptions which may need proof themselves; therefore it's 'safe' to assume that A isn't there. In other words, "the proof" is more based on probability and approximation, rather than a certain logical approach. Now this method may sound acceptable if you can increase the probability up to e.g. 95% so the 5% can be overlooked. But what if due to the nature of A, the odds cannot be devided that unfairly?