Well the protagonist in cells at work is always trying to do her work but always ends up apologizing because she gets lost and such failures to do her work hahah
In My Next Life as a Villainess: All Routes Lead to Doom! Not really trying to take responsibility and failing but she thinks she screwed up important moments and such and ends up apologizing, hmm...
In Keroro Gunsou there's this pair in which the girl always apologizes for his brother being useless constantly
That's the most I can come up with right now XD But if I remember more I'll tell you, my brain just started to come up with characters that just apologize xD