I doubt the game considers this something that's broken, and it seems like a deliberate feature of the game to me. Followers keep what you give them, but unequip it when they are not following, just as anybody takes off their combat gear when they are off duty. I've seen followers under attack instantly equip what they needed from their inventory, so for some people it may be this that's broken, not that they take their gear off in the first place.
I have never noticed such a thing...
Now I've had alot of issues both on PC and on PS3 so I guess it's just another bug in my game...
I've only seen them equip weapons, never armor.
Although like another guy said, dress up is fun. I would like to be able to pick their base gear regardless and I'm sure others would as well lol.