I've been single position training three guards, and in order to consistently get their full game in, I do the following depth chart
starting - backup - reserve
PG Trainee 1 Trainee 1 Trainee 1
SG starting SG backup SG backup SG
SF starting SF backup SF backup SF
PF starting PF backup PF backup PF
C starting C backup c backup C
Strictly follow and let them play for substitution and foul trouble choices.
This will help prevent weird substitutions if you have big blowout wins.
But, if you're trying to get 48+ min for three players in single position, there's nothing you can do if you suffer and injury or a foul out. That's part of the risk of doing single position training, in that when that happens, it becomes very hard to win your game.
In weeks where you have a game where your trainee doesn't get his full 48+, you'll have to decide whether to switch to two position training (in which case you'll want to plan beforehand what you would switch to, and where you should be playing your other trainees as backups), or just bit the bullet and accept the sub 48+ minute on your unlucky trainee.
A week or so ago I finally had a game that the pattern above didn't work entirely on. I had just gone up 22 with about 6 minutes left, and my starting PF got fouled on a shooting foul. Garbage time set in, and the substitutions occurred between the first and second FT, and since my PF was at the line for a second FT, the backup PF replaced my PG. It stayed that way for a few minutes - one time my player tried to recover a rebound and it went out of bounds, and no substitution, but I don't know if I've ever seen a substitution after that text. Then the PF got fouled on another shot, so that one didn't get to happen. Finally the backup PF got called for a shooting foul so he could swap to his proper position and bring the trainee back in. Odd turn of events for sure.
(http://www.buzzerbeater.com/match/39467419/reportmatch.as...)