B747-400 Captain reported temporary loss of aircraft control during a go-around.

Narrative

Low Altitude Go-Around due to sudden heavy rain over runway; sharp nose high pitch up.On approach; thunderstorms were noted in the area. Rain was observed passing over the field; with a cell a few miles south of the runway. However the runway was in sight at five miles on the approach; and was in sight until the flare. Wind was gusting; but the highest reported gust was 21 knots; at 070 degrees; well within limitations. During the flare; at an altitude of around 50 or slightly below; I lost sight of the runway environment due to a sudden increase in rain intensity; and elected to execute a go-around and missed approach. The aircraft was nose heavy; so the airplane had a lot of nose up trim. Upon going around; the nose pitched up; but I was able to maintain a normal pitch attitude with sufficient pressure. We executed a normal go-around; at around 1;000 agl I attempted to engage the auto pilot. Upon engaging auto pilot; the airplane immediately pitched up sharply and speed decayed rapidly. I immediately disconnected the autopilot and applied nose down pressure and began to add more nose down trim. Several attempts were made to engage the autopilot with the same result. It was not until around the fourth or fifth attempt to engage the autopilot that it maintained an acceptable pitch and airspeed. While pitched increased and speed decayed; it never did go below the maneuvering speed; and pitch did not exceed 20 degrees; as far as myself and the other crew members could tell. My recollection is that the takeoff CG and trim from ZZZ1 was 15/8.3 Units.I believe that the nearly 23 hours of continuous duty by time this event occurred contributed the haphazard nature of the go-around. I also believe that allowing for us to utilize the auto-land capability; especially when combined with long duty days and less than ideal weather conditions would help contribute to a safer operation.