Shortly after completing the quest "The Eye of Magnus", I decided to pay a visit to my homies in Whiterun. While using the forge of a very pleasant young woman who worked down by the city's main gate, my character increased his level to 21. Needless to say, I was absolutely thrilled and I rushed to my skill menu to start allocating some juicy new perks. What I found instead was that my One-Handed skill had mysteriously dropped from 54 to 15. I wasn't too concerned at first, thinking that it must be some sort of lingering spell effect or a glitch. I sprinted up the hill to the Shrine of Talos, paid my respects, and checked my skills menu again. Nothing had changed! Since then, I've tried everything short of restarting from an earlier save. I've dropped every item I own, excepting those important to quests, tried every major shrine available, I even worked my ass off to try and make a potion that could boost the skill temporarily. I'm playing on an Xbox 360 as a High Elf.

My undroppable items are:
-2 Amulets of Talos
-Balgruuf's Greatsword
-Dragonstone
-Pelagius' Hip Bone
-Stros M'Kai Rum
-Unusual Gem
And a butt-load of keys.