Over the course of a season most of the players on a team will drop a level, with the players at the high end tending to drop more than those with low levels.
Last season, playing time had an effect on stamina, and injured players could drop several levels when injured (because of 0 minutes PT). But they eliminated that.
You should probably get used to training stamina at least one week a season.
Next week might be a good week because of the draft. Drafted players won't necessarily have horrible stamina, but it might be fairly low, and unlikely to be proficient.