What system? Any mods? Do you possibly have several copies of the same suit in your inventory?Sounds like a jolly good ol' bug. When it's a Bethesda game: if it doesn't work, live with it.
4GB RAM (3 because using xp 32bit), dual core 3.1 ghz, GeForce 9600 GT. No, I have the same issue even with the winterized power armor and there isnt a copy of that anywhere else.
Try restarting a new game to see if that character has the same problem as your current one.
Started new game, the issue is till there.
However i did isolate the problem and it is a mod called Pipboy remover (makes pipboy invisible and prevents you from accessing it through F1 F2 and F3), which i installed after acquiring the Power Armor, in order to remove the annoying bare left arm.
I suppose my options now are to remove the mod and contend with the bare power armor arm eyesore or find another mod that allows me to set up more keybinds.