From a dumb user POV, I would say that it depends on frequency.
If I see a one off apology, for a one off issue, perhaps with a mild sense of humour, then that's good, I like that. I might even have sympathy.
If, however, I see a regular, frequent issue and get the same apology over and over again, it begins to feel insincere, and that they are trying to cover an inherent issue with an insincere apology, or humour. I then begin to feel that they simply cant be bothered.
If I see a one off apology, for a one off issue, perhaps with a mild sense of humour, then that's good, I like that. I might even have sympathy.
If, however, I see a regular, frequent issue and get the same apology over and over again, it begins to feel insincere, and that they are trying to cover an inherent issue with an insincere apology, or humour. I then begin to feel that they simply cant be bothered.
I think sincerity is the most important thing.