I think a true apology should include, among other things, a plan on how you are planning on ensuring that the thing you're apologizing for doesn't happen again. So my rule would be: if you're not planning on ensuring that this doesn't happen again (either because the system is working as intended or because you have no plans on fixing the issue) then any apologize will sound insincere (because it is).

When is an apology okay: "The site is down temporarily. We are working to bring it back online. Sorry for the inconvenience"

When is an apology empty: "Your train has been canceled. We apologize for the inconvenience", more so when you hear the exact same message thrice a week.