Need help saving toes!

I got a skink about 3 weeks ago, and it's having really bad shedding problems. It was already missing one toe and the tip of another, but now yet another toe is starting to turn black and most likely will fall off soon. The vet said to soak him twice a day in warm water. I've been doing that since day one. It has helped a little, but there still are toes I'm really concerned about. I've tried just about everything, mineral oil, shedding sprays, a humid hide... If I rub the toes with a q-tip, one of them started to bleed. This is a baby skink and if anyone can offer me any advice on how to save the remaining toes, I'd be so grateful! I was also told that he will most likely have these shedding problems his entire life Anyone else deal with this before?

Kate,

More than likely they'll fall off. It sounds like they are already too far gone. It sounds like you are doing everything right. Just don't be upset when/if they do fall off. I've had a few different animals (leopard geckos, skinks, etc) that I have received from people with bad sheds. Their toes have often fallen off and they are extremely happy, running around, etc. Just make sure you put neosporin/polysporin. Make sure they don't get infected and such. Wish the best for you and your's!

I kinda figured that. It's so sad, he's so young... I guess I'll just keep at what I'm doing and hope for the best!

Another thing is my BTS is really inactive, which worries me because he wasn't in the best shape to begin with when I got him. I've heard BTSs really don't do much, but could something be worng here?
Basically his daily routine is to wake up when I turn the lights on and bask for a little while. I purposely wait to feed him because otherwise his food will just sit out. He sleeps burrowed in a blanket and will come out on his own. After he's basked for a little while, he goes to take a drink of water and that's when I feed him. He'll eat and go back under the basking light. He'll sit there almost all day, occasionally going to eat more or drink more water. I have a humid hide set up for him to help with his badly shedding toe problems, but he almost never goes in. He doesn't ever use his hides either. The basking area gets up to about 100F, does it need to be hotter? I turn the lights out at 10pm and that's when he goes back into his blanket and sleeps until the next day.
The reason I'm asking this is because I had him out yesterday while I was folding laundry. He sat on my bed watching what I was doing in the same spot for about an hour. He didn't try to run away or anything. He's a baby, maybe 4 or 5 months old. He's alert and everything, just doesn't really do much.

I just need some reassurance that this isn't yet another issue I'll have to deal with. Thanks.