Are you asking about proofs of results where the result itself turns out to be false, or do you allow proofs with one part that was incomplete (a proof not covering all cases is strictly speaking not a valid proof of the claimed theorem) and the gap was filled in later?
The history of the Kronecker-Weber theorem provides an example of an incomplete proof that went unquestioned for a long time. Weber published a proof in 1886 and a gap was found in it and filled in 95 years later by Neumann. See the Wikipedia page about the Kronecker-Weber theorem. Arguably the reason nobody noticed the gap for so long is that, in the intervening years (starting with Hilbert ten years after Weber) other proofs and further conceptual generalizations of the Kronecker-Weber theorem were found, so there was not a strong incentive to recheck Weber's proof in order to have a proof of the result.
Again, if what you are really after is proofs that were fundamentally mistaken rather than being incomplete, this example I give does not fit. Please clarify your intentions.
Arguably, until a rigorous definition of real numbers and a proof of their completeness was found in the 1800s, lots of earlier work involving the real numbers was not fully justified. For example, Euclidean geometry needs further conditions related to continuity or completeness of the reals, which the ancient Greeks did not realize. Thus you could say there are 2000-year old examples in Euclidean geometry, and you'd be hard-pressed to find examples over a longer time period than that.