How many green bars are your players showing before training?

When you go to train a player, click on the button that says "Set Team Intensity" and make sure that your players are either set to Normal or Hard, as if they are set to Rest they won't train even if you select a training option.

If your players have 1 green bar in their intensity option that means they are resting and they won't lose condition or improve as a player as a result. If your players have 2 green bars that means they will train at a normal level, whilst at 3 green bars its on hard.