A320 Captain reported loss of automation including autopilot and auto throttles in cruise. The flight crew continued to destination airport and landed.

Narrative

I was the pilot flying (PF) on a flight ZZZZ-ZZZ. Approximately 35-40 minutes after takeoff; and shortly after reaching top of climb at FL380 and still speaking with ZZZZ Control; we were both alerted to the Master Warning and Master Caution alerts going off. This was approximately XA10.We discovered that both the Autopilot and the auto thrust had kicked off; and we both lost flight directors and the First Officer's (FO's) Navigation Display (ND) was showing in red MAP NOT AVAILABLE. I took over hand flying the airplane and adjusted the thrust levers to match the necessary Engine Pressure Ratios (EPRs) to maintain altitude and speed. Knowing we were in RVSM airspace I directed the First Officer to request a descent to FL280 while we tried to sort out the multiple issues presented.As we leveled off at FL280 it became immediately apparent two things. One; our fuel burn was significantly higher as we were originally filed for FL380 and two; there was a large line of thunderstorms approaching us as we neared ZZZZ1 airspace. I scanned my ND to consider a divert to ZZZZ1; our nearest station not behind us; and saw that there were multiple cells painting in the general area. Returning to ZZZZ was not an option; as we were battered by fairly large cells on the inbound trip on the ZZZ XX STAR.I concluded that the safest option was to climb back into RVSM airspace and maintain heading and altitude by hand while we attempted to troubleshoot the systems and bring the automation back online. It was roughly XA00 local time; the TCAS showed no airplanes in the vicinity and the radios were dead quiet. There was no conflicting traffic to contend with.I briefly discussed with my First Officer whether or not to [request priority handling]. In the end I felt it was probably going to cause more trouble than it solved; as the airplane was under control; we were safely above any weather and we were for all intents and purposes continuing as if nothing had happened.At some point over Area the systems came back online by themselves; we found that we could engage the Autopilot and the auto thrust and both flight directors came back online. We left ZZZZ1 airspace under full automation; although ZZZZ1 Control did query us as we were nearing ZZZZZ about our altitude; as he was showing us some 200 ft. low. Both my First Officer's and my Primary Flight Display (PFD) were reading FL340; and the standby indicator was showing a little high; about FL341.Shortly after entering ZZZ airspace we lost all automation again. We were on the ZZZZZ1 arrival and; as is customary on that arrival; given direct to ZZZZZ2. I told ZZZ that we had lost automation and all we could accept was headings. The phrase 'we're basically a big Piper Cub' was uttered; meaning we were simply stick and rudder at the time. The controller gave us a heading of 024 degrees which was an intercept vector for XXR and gave us a descent to 7;000 ft. During the descent the automation once again availed itself; which we activated. By this time we had lost automation multiple times; each time eventually getting it back. We intercepted the glide slope uneventfully for XXR and I manually disconnected the Autopilot and auto thrust; not wanting to be surprised yet once again by a finicky system.The landing was uneventful and after a short wait we taxied up to the gate and parked the airplane. Maintenance was notified and the logbook entry was made.