I think this happens. Bitshares has faced this challenge, since its security model, DPOS, has nodes that are permitted to mint voted in by an (apathetic) voting body of shareholders. It has become gradually more difficult to be elected as a Bitshares delegate, because voters have become more apathetic over time. It’s sometimes even difficult to vote out a nonfunctional delegate.
I haven’t seen this become a serious issue in NuBits, which is the most prominent Peershares implementation so far.
Interestingly, something like this happens in world democracies, too. Voters become apathetic, and inferior leaders get elected. (Not quite the same phenomenon, but hey, it’s something to think about.)