It makes me feel like they're trying to minimize or discount my own feelings (of disappointment, anger, betrayal etc) to present themself as a victim. To me, an apology doesn't really mean much. It's just words. If you apologize, then continue to do the same thing that elicited the need for the apology in the first place, then you're not really sorry. You're just apologizing to get me to stop being upset/confrontational/etc.
Say 'sorry' once, but demonstrate you're actually sorry by changing your behavior. Otherwise, you're just repeating false platitudes in order to dismiss my own feelings.