For the "repeated apology" person, you should press them to commit to "never happen again." That is a totally reasonable request, and therefore does not make you sound ungenerous, unforgiving, or 'no fun,' which is the main advantage that that person has over you. And once committed, they risk the ambarassment of becoming a liar, which you can press on them again and again if need be.
In general, apologies magnify the status of the apologist, make them look 'good,' so they play that game for that purpose. It happens all the times, as when recently I saw a male news anchor make a sexist joke on his female colleague, and immediately turn around and say 'you know I was joking!' with a stupid alecki smirk on his face. He showed himself to be a 'fun' person, a politically conscious person, and an ennobled appologist to boost. All that at the expense of his female colleague who, what can she do? could only manage a meek smile for the moment.