B737 First Officer reported an autopilot disconnect malfunction during an autoland approach at low altitude. The flight crew performed a go-around and returned to the airport for a successful autoland.

Narrative

I the First officer Started the leg segment as pilot flying. The flight was uneventful until approach was started. As we got closer to ZZZ the weather conditions continued to deteriorate. We both discussed and decided that Autoland would be the best course of action. We decided the captain would take the controls. We briefed that if the conditions improved that I would take the controls back and complete the segment. After a positive transfer of controls; we briefed the Autoland from the briefing guide. Went through and talked about different expectations and threats about Autoland including the go-around. Then conducted a full arrival and approach briefing. We had all the required equipment. We set up for runway XXR. After we received landing data we decided due to being a shorter and wet runway we would do flaps 40 and auto brakes 3. As we begin getting vectors ATC notified us we would be vectored thru the approach course for separation. We rejoined the approach and engaged the second autopilot. We were completely configured flaps 40 at target airspeed with the landing checklist complete by 1;500 ft RA. All FMA annunciations were correct. The appropriate call outs were made. As we got closer to the runway about 50-70 feet RA the autopilot disengaged. We both experienced the startle and surprise affect. The aircraft nose pitched down quickly. The captain applied back pressure to the elevator to arrest a higher than normal descent rate. The aircraft made contact with the runway which resulted in a bounced landing. We commenced a go-around and all of the callouts were made. During the go-around HDG mode would not engage; we recycled the flight directors. We overshot our heading by about 15 degrees. I ask for the aircraft to come left as HDG as mode was restored. We started to increase speed; I called Check Speed" which was promptly corrected. We were expecting a published go around procedure but received a different heading and altitude. ATC asked for a reason for go-around during a high area of vulnerability. I asked them to standby. When we got established downwind and in a medium area of vulnerability we discussed fuel; our alternate; spoke briefly about what happened; and plans for the Autoland if it were to disconnect again. I also brought up on the bounced landing the off-scheduled light illuminated. We went through the procedure and the aircraft was confirmed to be set to the correct elevation. We reprogramed the FMC and set up for a second approach. We did not get a chance to make a PA to the passengers or call the Flight Attendants. During the second attempt we were fully configured flaps 40; landing checklist complete; FMA normal by 1;500ft RA. The second attempt was successful and uneventful. After the flight concluded we had a very thorough debrief that included the entire flight from start to finish. After we ran the termination checklist we debriefed on what went wrong with the Autoland and the missed approach and also what went well in regards to handling the startle and surprise of the autopilot disconnecting. We spoke in great detail of the missed approach and the Autoland procedure. We spoke about our high angle of attack during the bounce/go-around and the potential for a tail strike. Due to the possibility of a tail strike the captain did conduct a post flight exterior inspection and found no evidence of a tail strike. I did learn a lot about the Autoland capabilities; vulnerabilities; and how to be more aware as a pilot monitoring. The captain debriefed the Flight Attendants; and the outbound captain. Throughout the entirety of the flight the safety of the aircraft or the passengers was never in jeopardy. All SOP's were compiled with and a safe go-around was initiated. In conclusion I believe we handled the situation well. We communicated as a crew and put the flight path first.During a go-around from XXR in ZZZ; ATC issued instructions for an altitude of 2000 and right turn to a heading. Immediately after I was asked for a reason for the go-around. Due to this being a high area of vulnerability I asked ATC to standby. During the go-around I was the pilot monitoring. As we did; our call outs heading mode would not engage. I recycled the flight directors and reselected HDG mode. During this time we passed our heading by about 15 degrees. I stated the aircraft needed to come back to the left and it was promptly corrected. This was a brief and minor deviation. We were never informed of any deviation. I take full responsibility for the deviation."