Yes, the stars only stay the same if you don't promote.

One thing to try to do is improve your facilities,
keep building as soon as one build finishes start another.

You get green and red boosters, which are vital for fixing injury
and the green for adding extra training to your better players.

Try to get high value players when you add to your team,
you want the faster trainers if you want to keep them some time.
I watch when the designated trainees are close enough to attain a point,
they get a green and train on hard when doing training.