A321
Flight Crew Air Transport Pilot (ATP)
Aircraft Equipment Problem Critical; Inflight Event / Encounter Fuel Issue
Flight Crew Executed Go Around / Missed Approach; Flight Crew Overcame Equipment Problem
Weather; Aircraft
After an extensive hold while approaching minimum fuel we were cleared for an ILS. The captain and I agreed that we had adequate fuel for two attempts at landing before necessitating a diversion to our flight planned alternate. The weather dropped below minima necessitating a go around. A go around was executed and performed per company policy and standard operating procedures. Once ATC vectored us off of the missed approach the captain began to reconfigure the FMS for our second attempt. We received a series of faults in rapid succession that ultimately resulted in a non-recovering dual FMGC failure. We notified ATC of our primary navigation failures. As we held we began approaching minimum fuel; while negotiating weather; and attempting to problem shoot the multiple failures. After a brief time we were able to reload the FMGC and input our destination and the appropriate approach. However; the FMGC would not accept the Cruise altitude input to force the FMGC into cruise mode. It was returning an error message. In effect it was stuck in takeoff mode; and would not sequence to later in the flight. After a brief discussion we decided to attempt to quickly advance the thrust into TOGA and then return to the climb detent and rebuild the automation.I pushed the thrust levers to TOGA; and immediately returned them to the climb detent. The aircraft began climbing as expected; I selected altitude hold; and pulled selected speed. The autopilot did not acknowledge my inputs. I attempted each multiple times. In order to prevent an altitude deviation; or a flap overspeed I disconnected the autopilot and engaged manual thrust. At this point everything was stabilized. We had not deviated from our altitudes; heading or assigned airspeeds. We reselected the vertical mode; and received an altitude capture. We reengaged the autopilot. I returned the thrust levers to the climb detent expecting the auto thrust to recapture. I noticed that this did not happen; and retarded the throttles. Moments later a minor flap exceedance was experienced. Fortunately; this maneuver properly sequenced the FMGC and we were able to continue our approach to landing.  Upon landing we entered the FMGC failures as well as the flap exceedance into the [maintenance log]. Multiple complex system failures; during critical phase of flight; with adverse weather; and near minimal fuel considerations.
[Report narrative contained no additional information.]
A321 Crew reported a problem reprogramming the FMGC after a missed approach.