Come to think of it, doesn't the Unofficial Oblivion Patch already come with a selectable torch hotkey icon at the bottom of your inventory list? Or is that added by OOO?
Probably OOO. I don't see it in my inventory list. I updated UOP to 3.4 from tesnexxus. It added a separate .esp. No change that I can see.
It means reinstalling the game, right?
For the binding issue? I don't think so, I wouldn't.
In my case, it turns out to be a save game corruption. Loading an earlier save confirms that torches remain bound. So there's nothing wrong with the game engine. This is probably true for you as well. If you don't mind loading a save from before you noticed the problem, you'll probably find the same thing.
One strategy is to load a save from last week and see if the torch remains bound to your hotkey. If not, load from two weeks back etc. Try to narrow down when the glitch occurred. Hopefully it happened recently and you don't lose too much progress or time.
The other option, the one I'm considering, is to just live with it and install one or both of the mods recommended by Decrepit and Viper.