It might be less of a small bounce than the nose wheel not being on the ground and/or not having enough weight on it. I know Airbus and Boeing handle this differently, but I don't remember the details (I want to say Airbus allows reverse thrust once the mains are firmly on the ground but the nose isn't, but I need to check my manuals).

I really do find the inability to restart extremely interesting though. I'd bet it's a bug somewhere, but it would be alarming if Boeing programmed in a lock-out on the failed engine(s) (I've heard it talked about as a solution to the sudden deployment of reverse thrust in flight) .