Regards the whole training thing, how hard a player trains is determined by his determination rating.
As someone else mentioned, age is also a factor. Players under 23 improve much more than older players, while once players get into their mid-thirtys, they get worse. Although this can be staved off for a while by the training, you can sometimes see a disasterous drop-off in ability, especially in areas like stamina, pace, strength, etc.