Stargate SG-1, Season 4, Episode 6 has a variant of the loop trope, but everyone (including most of the protagonists, and everyone else on earth) don't remember what happens, while two protagonists remember every loop until they are able to stop the looping.
They debrief the others who don't remember at the end (except for the things they did when they took a loop off anyway!) - but they didn't miss too much since everyone else on earth missed it.
Another fictional work - a book, not a movie / TV show / anime - is Stephen Fry's 1996 novel Making History. The time travel aspect is questionable - he sends things back in time to stop Hitler being born, but no people travel through time. However, he remembers the past before his change, and has to deal with the consequences of having the wrong memories relative to everyone else.