What you are referring to is known medically as dysecdysis (at least one form of it). It can be caused by a number of factors. I'm sure I won't think of all of them, but here are a few to get you started:
1) Husbandry. Temp/humidity/lighting/furniture can all be potential problems. You did say you are housing the problem skink with another animal that isn't having problems, and while that makes husbandry seem a less likely culprit it doesn't necessarily rule it out. It could be that the problem animal has an underlying health issue (which we will get back to) that makes it more susceptible to problems arising from improper husbandry. And since husbandry is the easiest thing to fix, I would go there first. Check all of your husbandry parameters again. Even the ones you're sure you don't need to. Note: UV lighting has been successful in halting dysecdydsis from unknown causes in a number of snake species. It might be worthwhile to add some UV light if you're not already using it. No help here? Move on to Possible Cause Number Two:
2) External parasites. Mites especially, but also ticks and other external parasites are often the cause of abnormal molting. Check closely, especially around eyes, mouth and cloacal opening for parasites.
3) Metabolic/diet issues. MBD, hyper- and hypovitaminosis, and hyperthyroidism have all been known to cause dysecdysis. These are ailments that you probably won't be able to diagnose yourself. A blood panel done by your vet should reveal any of the above problems. Malnutrition is another cause, but one you should be able to recognize on your own.
4) Dermal fungal/bacterial infections. No explanation needed. Again, see a vet to diagnose.
5) Mystery ailment. There are many cases of dysecdysis for which a cause is never identified. The problem is that ecdysis is a process that uses some of an animals energy stores (to create the replacement skin), and continual molting may stress an animal, miking it immune to other ailments. IME with snakes that suffer from this form of dysecdysis, animals that go undiagnosed and untreated have shorter than usual life spans.
I realize that I've just given you alot of information, and not much help. My advice would be to check what you can on your own and then seek help from a vet if you can't correct the problem. I wish you luck.
-Z