Yes, it is reasonable to infer X on lack of evidence for not X, under specific contexts but not in general.
Suppose you see a hundred crows, all of which are black. You would be reasonable to infer that all crows are black (maybe even going so far as to define a crow to be black, including it in the defining characteristics). This works in the bayesian statistical inference method. But that is no guarantee that absolutely no crow will appear that is not black.
This is related the hypothesis about the closedness of the set of data under consideration. One can assume the Closed Word Hypothesis, which means, in the set of data at hand, if A does not appear, you are allowed to infer (or really, you know) that -A is true (or -A must appear). The Open World Hypothesis says that you only know of things stated not about unstated things (but then Bayesian methods apply, you get more and more confident that -A is true the more times you do not see A).
It is a classic blunder of Hegel's (sorry, a classic myth about Hegel) that he said that there could be no more than seven planets, and in the same year as this proclamation, another planet was discovered. (It's so much more complex than that: the 'planet' was Ceres, Hegel 'proved' that Bodes Law was not correct not that there were no planets beyond Saturn, but the asteroid belt (which Ceres is a part of) fulfills the numbers of Bode's Law.)
But anyway, there are some negatives you can prove and some you can't. You can prove that there are no primes that are both even and greater than 2. You can't prove (experientially) that there an X (with consistent properties) doesn't exist in an unexplored area.
Then again, here is the classic informal disagreement between Russell and Wittgenstein, where Wittgenstein claimed that there is no evidence that there is not a rhinoceros in the room, and Russell took a more practical tack.