@Amortentia
There are actually very specific times when I also refuse to apologize. Like if I feel like I do something at work that is the proper course of action given my judgment (maybe calling a meeting about an important issue?) and someone complains because they felt my action was unnecessary, I refuse to apologize... since I don't want to put myself in a position where I feel uncomfortable doing the same thing in the future.
@BrianL
I respect your right to apologize for saying sorry too much. It's okay to be sorry for saying sorry, if that's how you sincerely feel on the matter.