Well, in my case, I'm loosing the last quarters often too when my team has a big lead... In last quarter, my coach puts in the back-ups, while the opponent plays with his starting five... And even then, my team doesn't look bad... But I never noticed some big influence of stamina... Check this game:
(8683502)And three of my best players here have stamina as follows:
Tulic - awful
Villalobos - inept
Tuponja - pitiful
And I always play a fast paced tactics... So, I don't have some good reasons to train stamina yet, maybe when my players become too old for training...