A321 Captain reported an air data malfunction resulting in a low airspeed indication during a cruise climb. The Captain leveled the aircraft and descending to a lower altitude and continued to the destination.

Narrative

Previous write up for Captain AOA vain fault had been cleared twice on this day. Multi-Mode Receiver (MMR) 2 issues were caused; noted; and cleared by Maintenance during AOA repair. Unknown if those are relevant issues as there were no indications at the time of the incident. Uneventful preflight and takeoff after Maintenance sign off. After an initial level off at FL270; the Captain started a climb to FL330 using open climb. Initial indications looked good and the Flight Mode Annunciator (FMA) was set correctly. The aircraft pitched and started to climb at around 1400 ft per minute. Even though the FMA showed it was in open climb; the aircraft held approximately 1400 VVI. The airspeed slowly decayed from 318 KIAS to 268 KIAS. The crew was busy considering a deviation for a building storm approximately 100 miles ahead and the radios were busy with aircraft requesting deviations. First Officer (FO) noticed when aircraft was initially approximately 5-8 kts. slow but thought the aircraft was still accelerating after the level off and dismissed the observation without saying anything. After more deviation discussion and radio calls; the FO's scan returned to the airspeed and noticed it was significantly closer to VLS and still decaying. A quick scan of the FMA and Autopilot/auto throttles did not give a good reason and the FO asked Why is our airspeed slow?". This was around 270 kts. and the Captain recovered the aircraft by manually leveling off and eventually descending back down to FL310. The crew noted the Autopilot disconnect warning light and sound when the Captain recovered. There was no warning or status message prior to that time. After stabilizing the aircraft; the crew attempted to re-engage the Autopilot. The crew had a Autopilot 1+2 INOP and CAT II INOP messages on the status page. These cleared themselves and then the crew was able to reconnect the Autopilot. The crew ran the unreliable airspeed checklist as a precaution and found all indications to be in line with what was expected. The crew continued to ZZZ being extra vigilant in monitoring the Autopilot. Later in The flight; the crew got indications of a MMR 2 failure as well as indications of the Captain AOA failure. The crew landed uneventfully. The crew wrote up the incidents in the logbook and the Captain provided an extensive debrief to Maintenance personnel at the aircraft and a Maintenance supervisor via phone. The data can be seen and corroborated in the safety software. It appears Maintenance signed off this write up by performing an ILS CATIII test; which would not appear on the surface to address the situation. The unknown nature of why the Autopilot did not perform as intended is what gives the crew member hesitation and a desire for further investigation.Cause: Unknown cause of the event. FO could have spoken up when deviation was approaching 10 kts. from target airspeed without an explanation. This would have made for a less stressful recovery with a higher airspeed margin."