We're running two 5555-X ASAs in HA mode and started experiencing this issue almost a month ago.
Conducted extensive troubleshooting with CISCO TAC over the last three weeks. Plenty of packet captures, DART logs, etc were provided, before arriving to conclusion that version 9.12.1 was the cause.
Upgrading to 9.12.2 provided temporary improvement, however intermittent connectivity issues were still taking place. Yesterday we've upgraded to 9.12.(2).4 (Interim release) and everything seems to be back to normal.
