The subs situation is really very poor. Only having 3 was already bad, but now with this stamina issue its critical. However, making even 1 sub in-game is an absolute joke - you can try and rush it during a corner or a throw-in, but even then with the speed of the clock you're away for sometimes 5-10 minutes of game time, during which - guess what - the AI is so poor that you concede a goal. Making 5 subs in-game would pretty much mean you're not playing any time and just hoping your team isn't picked apart. Which is not why we play the game - there's Manager Mode for that.
If EA insist on sticking with this stamina strategy, then they also need to do something that allows subs to be made without basically guaranteeing you'll lose the game. Time-outs arent really part of the IRL game but it would be a start here.