Air carrier flight crew flying A321 aircraft reported pressurization malfunction. Flight crew diverted and landed uneventfully.

Narrative

Ground operations; takeoff; and departure proceeded without incident. The Captain served as the flying pilot; while the First Officer acted as the monitoring pilot. Upon climbing through Flight Level 330; I noticed the cabin altitude flashing; indicating a pressure altitude of approximately 9;200 feet. We initially requested to level off but then opted for a descent to 31;000 feet. As cabin pressure continued to rise; we informed ATC of a cabin pressurization issue and requested a lower altitude to resolve the problem. We were assigned Flight Level 270; at which point I donned my oxygen mask and called for the Quick Reference Checklist (QRC) for high cabin pressure; specifically CAB PR EXCESSIVE CABIN ALT.During our descent to 270; we received an ECAM notification for excessive cabin altitude. We completed the memory items; and I called for the Emergency Descent QRC. We requested a descent and were initially cleared to Flight Level 200. As we descended; I asked the First Officer for the nearest airport. He mentioned ZZZ1 and ZZZ. I decided to divert to ZZZ and asked him to coordinate the change in destination and request a lower altitude. We were subsequently assigned 17;000 feet.As we descended to 17;000 feet; cabin pressure began to recover and normalize. We informed ATC that our cabin pressure was normal and requested to maintain 17;000 feet. We were approximately 180 miles from ZZZ. We completed the QRC and QRH procedures for the non-normal situation as outlined in QRH. We determined that an overweight landing was unnecessary and then swapped control of the aircraft.I first called the inflight crew to update them on our situation; instructing them to discontinue service and prepare the cabin for landing in about 20 minutes. I then contacted our dispatcher via satellite phone to report the pressurization issue and our diversion to ZZZ. While on the call; she connected me with our maintenance controller; and I briefed them on our situation and intentions. The approach and landing were uneventful. We landed at approximately XA:00; but a gate was not available until XB:30.Upon arrival; we were met by the emergency response team in ZZZ; and we informed them that no further assistance was needed. When the gate became available; we taxied to it and disembarked the passengers.On the previous flight; there was a write up for pressurization. Left aft service door; found by contract maintenance in ZZZ. There was also evidence found in ZZZ the door seals were excessively lubed.