Once AOA-prot is passed, the aircraft changes into a flight control law where stick neutral commands AOA-prot and full-back-stick commands AOA-max.
In older ELAC standards, if the passing of AOA-prot was only a temporary thing (for example a short vertical gust), the aircraft would still keep this law, meaning to pitch-up into AOA-prot if stick was neutral, since after passing AOA-prot, flight control law changes, and stick neutral commands AOA-prot, although the AOA would be way below AOA-prot after the vertical gust has passed. To leave this law, some fwd input on the stick is needed. However this is intuitive, since any reasonable good pilot would pitch the aircraft down, if it suddenly begins a climb.
On newer ELAC standards, if AOA goes by itself back to values below AOA-prot, the aircraft does not anymore pitch up to maintain AOA-prot, but leaves this law without stick input.