Nope unfortunately you just have to pray for him to get his full minutes. The game is not designed for players to play 58 mins a game and that's why it can he hard at times to get just that.
It certainly isn't designed for 58 minutes a game! ;)
The only thing I can add as a possible workaround that in and of itself is untested is that if you know it's going to be a huge blowout, maybe have a second, non-trainee player with terrible stamina (ideally worse than your trainee) play a full 48 with no bench players behind him (and thus only dressing 8 instead of 9 if one position training). The hope then might be that when the starter cycles in, maybe he'll replace that guy instead.
But that's something I haven't tested and would not be surprised if it also fails. ;)