I have suggested that simply playing in games should have an effect on stamina.
There could be some target level such as 64 minutes equals strong, 56 respectable, 48 average, 40 mediocre, 32 inept, 24 awful, 16 pitiful, 8 atrocious.
Playing that many minutes in a week would cause stamina to change some % (10%?) towards the target level. However, a player who plays above 48 minutes would never lose stamina.
Someone who was at average stamina and was injured for 7 weeks, and then played 48 minutes for 7 weeks would lose more than he would recover, but at least it wouldn't be a case of having to train stamina for the one player.
The announcement suggests that there will be a difference between playing 45 minutes and playing 0 minutes due to injury.
"5) Stamina will now decrease during weeks when a player plays too few minutes and during injuries, so as to encourage teams to regularly train it rather than just doing so once."