Timeloop story often linger on each iteration because most of the time, the only thing that carry over is information, the beginning of the timeloop is going to be redundant information most of the time, and the information from previous loop usually help the looper to stay alive longer in the next loop, which in turn allow them to gain more information.
But since there is absolutely nothing she can do to prevent her death, she's pretty much fucked whenever the entity take over, and she can't do anything about that either
While I agree with you, not all time-loop stories use their time travel mechanics to "arm" the protagonist with information.
I am aware
I am being a pedantic fucker but two examples that come to mind are
Steins:Gate, that uses time-travel as a framing device for the different routes in a VN. And (my favourite misery porn)
My fiance is in love with my little sister (
the manga and
the WN) where the long time spent in each iteration only serves to push the protagonist further into despair. And the deaths are only the author sadistically pulling the knife out and raising it high in preparation for the next time (s)he'll stab you.
In neither examples can I argue that the protagonists use information from the previous loops to "solve" their predicament and survive their fate. Both examples more or less are solved via deus ex machina. But each one still takes it's time for each loop.
A great example of the kind of story you're describing, that pops in my mind because it's currently ongoing, is
Akujo Kyosei Keikaku (
here), and that has
looooong stetches before each reset. Great characters and great scheeming / long time planning by the time-travelling protag.
Finally in this manga too the protagonist gains new information each loop and is trying to unravell her situation to survive longer. It's just happening at a much quicker pace because the only option Cecilia has to gain information is to interact with Milphina directly or her attendants... both of which will result in her death each time. And the time frame over which she reincarnates is very short, she's explicitly not given enough time after reincarnating to be able to make any kind of move.
It's great!
Boy I am rambling.
tldr: I don't have any friends to talk to about this stuff and used you as an excuse to organize my thoughts in writtting. Reply to this post at your risks and perils.