I used to run more full court press with lower-stamina players and I also noticed that I would lose a lot of ground late in games. I've trained stamina a couple of times, and now that my star players have decent stamina across the board and I don't play full court press, I tend not to kick away games late anymore.
Of course, playing TIE means that your guys won't hold leads well either, and it partially depends on the team you're playing against and whether you're at home. But it's definitely a bad idea to ignore stamina.