All stats decrease slowly when a player has a certain age (something around 32).
However, stamina is the only skill that ALL players lose during the season. I've read before that 1-2 weeks of stamina training are definitely enough to maintain (probably even slightly improve) the current stamina level of all your players.
The best time to do this is during the All-Star break and Off-Season when you have only 2 matches in a week. Or you could do it in a week where you completely messed up the minutes for your trainees.
We have both said a lot of things that you are going to regret.