That does seem to be the line of reasoning ... but
it doesn't make absence of evidence evidence of absent,
it just changes the rules.
If you are looking for something (A) in a well-defined search space
and you know that you have covered 100% of that space without
finding (A) then the absence of (A) has been shown.
If you have not covered 100% of the search space, you have not
shown the absence of (A).
You may, as your coverage increases, become convinced that you
will never find (A) ... but the accumulation of failed searches
does not amount to evidence that (A) is not present (nor that
it IS present).
I think what is beign suggested is that the longer something
remains absent of evidence, then that builds a case for
the absence.
This is not true. One can never rule out that one is
looking in the wrong place or for the wrong thing except in the
extreme case where the issue is so well defined that the
entire search space can be investigated with 100% coverage and
100% certainty of success were IT there.
E.g. the football field -- we cannot say the field is absent of
a football until we have searched every football sized space
on the field.
Things are always in the last plave you look for them