In fact, I noticed this trend of many time travel stories: the male protagonist can go so far only because of a female character.

The oldest example of the timeloop sub-sub-genre in anime that I can think of, the original Higurashi/When They Cry, gives the male protagonist around a half-dozen female helpers, and everything since seems to have provided at least one. (Higurashi did mix things up a bit by having the odd loop where one or the other of the girls ran violently off the rails.)