I have the same problem.
I have my best player a special ability. But I have paused it atm.
Now I have 2 problems:

He doesn't get any skills after a game. Just like you!
And if I train him, he almost get no skills. Normally het get 9 to 12 skill points after 4 or 5 trainings. Now I am lucky if he gets 2 or 3 kills points after 4 a 5 training sessions. He is only 22, so it is not the age.

Is there something or someone who can help me with this problem?