Well, yes, they do lose their stars every Season, unless you do not promote to the next level League.

The faster trainers will just about keep up their star level with little extra training. (using green packs to keep condition up) The fastest of trainers can easily keep their stars up for a couple Seasons, so it can be worthwhile if you don't want to be always changing out your team, to buy the best players you can, four star players can be excellent too.