Is there any downside to keeping a player on the DL after they are well. I had a young, promising player go down on my ML roster, but he was only a part time player.

The health and durability of many of my players is questionable. I'm guessing someone else will DL soon. I'd like to keep him on the DL until another player goes down.

I've seen the Yankees do this in the real life, but I don't know if it will work here.

The biggest downside is that the player will lose all that development time and he will not get any better while you have him on the DL. If you don't want to demote him you have a few options. If you called up a player to take his roster spot, you can activate your guy and demote the guy you called up. As long as you called him up at the same time you DL'ed your other guy, he won't take a ratings hit. Your other option would be to waive a vet who isn't contributing much and might be overpaid. He will probably clear waivers and you can demote him and if he doesn't you shouldn't be worried because the contract will be off your books. As a further note, if your guy is a promising player find ways to get him into games so he will continue to develop. I've seen really good prospects stop developing early because guys promote them too soon and they don't play them enough.