I'd say in general you're better off with some kind of set training schedule... or at least an idea of which players (5 or fewer at 1-2 positions is best) you want to train each week. Most skills take more than one week to pop, so if you're training a different skill every week (and for different players) it is entirely possible to go a long time without any pops.
Just as an example, if you're training one-on-one for guards, that should produce pops in driving after 2-3 weeks, handling after 3-4, jump shot after 4-6, and inside shot after 5-7. There's a thread dedicated to the amount of time it takes to get pops with different types of training.... I'm sure someone else will post it here at some point, otherwise I'll go hunt it down.
As far as DMI goes, it is highly dependent on game shape. Also, it doesn't particularly matter if it goes down, just as long as it changes so you know that training has occurred. If your player's game shape goes down, though, his DMI will also go down.
What level is your trainer? In Div V, the absolute maximum you would need is a level 4. Anything above that is probably a waste of money due to the huge salary and huge signing bonus.