So far, I've only been unable to use my weapon if I didn't pick it up in a previous room. No problem if I remembered to recall it before transitioning.
Recall is assumed to be at fault here because of the above mentioned bouncing noises upon pressing the attack button—apparently from the ring(s) hitting a nearby wall, trying to return to you.
In my testing up to now, two factors seemed to play a big role in the bug:
a) Firing a shot in the room with the stairs and not recalling it leaves me unable to shoot in the next level's starting room (the one with the little pedestal) in 100% of the cases, leading to the known bouncing sounds. Everything resumes working correctly once I enter any connecting room.
b) Performing at least one ”Rite of Multiplication“ is guaranteed to leave me defenseless in an enemy room if I left my rings behind in the directly preceding one on the same floor or the stairs room on the preceding floor. The latter scenario trumps what I described in a). Failing to recall multiple rings in the last room of the previous floor completely locked my out of firing in the next arena, even though I crossed an empty room (start of the current floor) beforehand.