Stamina links with DMI and they feed into each other. But also I think DMI is affected by compatibility in style of play to personnel and by how each player is being used. Also I think in some way teams and players will go into each week with a different mindset. DMI is a predictive feature based upon how a player practices, therefore if your going into a light week then DMI could trend lower just because the players will know they don't have to try very hard even if the minutes were well distributed the week before. I also think a challenging week can make DMI ratchet because of what awakes, and can even do so if the minutes from that week before.
As to training stamina, I give it a week once a season, sometimes once every other. But I also keep a solid 8-9-10 deep rotation stocked with players who can be moved around. So my minutes per starter stay in the 30-38 per game with 30 minutes each for backups who are slotted in two positions, the single position sub gets around 12-18 most nights.
Now if I was say six or seven deep and had guys regularly logging 40+ a night then stamina would be more of a issue. It is however the most meaningless attribute on the game IMO