I'm posting here because it seems to be the only topic specific to this model on the forum and I don't want to start a new topic for a seldom seen meter. It should also apply to the MX50 and MX51 models.
I dug my MX52 from whatever was on top of it, pushed the power key to see it blink the display and not want to come back on. Battery measured 2.5V.
Inserting a fresh 6LR61 brought it back instantly, then when I wanted to switch it back off it was stuck on, insisting a while it would turn off sometimes, sometimes came back on by itself.
Current draws measure 1.2 to 4.5mA (The true RMS conversion is greedy!) when on, 9 to 11mA when off!
I replaced both 1µF/35V tantalum drops (one on each PCB), power switching Transistor Q1 (BC857B marking "3F") on main PCB and capacitor discharge transistor Q13 (BC847B marking "1F") on display PCB under LCD. Both were in low melting temperature plastic packages.
I'm not saying it's fixed, only time will tell for sure.
Standby current draw is now down to the 10-20nA range.