This is probably something which is supposed to happen, rather than a bug in the technical sense, but:

If (whilst playing Strife using the original EXE) you are in God Mode, and go through a toxic / radioactive area for too long without wearing an Environmental Suit, at some point (presumably, when you would have died were it not for God Mode), the poisoning becomes permanent and the inventory left/right keys become disabled.

Playing using ZDoom fixes this questionable behaviour.