A gene isn't one bit.
For starters, there are four nucleotides in DNA (A, C, G, and T). Simplifying our model of mutation to "a flipped bit" where mutation takes takes a nucleotide to another one with equal likelihood, and only one nucleotide in that position makes it functional, there is a 3/3 chance that a mutation breaks it but only a 1/3 chance that a subsequent mutation fixes it.
Next, there's the fact that every gene is a sequence of many nucleotides. The odds that the next mutation of the same gene would happen in the same place is low.
Finally, many mutations don't take the "flipped bit" form we assumed above. Repetitions, insertions and deletions also happen, and may be even less reversible (deletion of a meaningful portion would be exceedingly unlikely to be recreated by chance - what provides the information about what should have been there?).