I'm pretty sure it can.
For example, you were training JS and each training increased JS sublevel by 0.1. But if the drop in sublevel of JS was 0.2 every week, then although you're training, the result is still a drop in a skill.
So I suppose once the rate of decrease in a skill is faster than the rate of increase in a skill, then all you're doing by training is to slow down his rate of skill drops.