I'm later still to the game, but I also had problems with the PM55A (and I have mentioned the problems with PM55A on the forum). I own two of them, one bought, one found in a trashcan (no, really!). They are utterly unreliable with constant "restarts" and who can have confidence in a meter that actually have an "reset" procedure printed on the back?
But I may have a "fix". Instead of one CR2032, try two CR2016. It seems almost like the design had two batteries in mind. Of course, this "fix" more than halves the battery life and doubles the battery replacement cost, and 6 volts may still be too much for the design. With two 3 volts button cells, the constant restarts, confusion in auto mode and such disappeared and the meters seems stable. But still, I seldom use them anymore, since I don't really have confidence in them anyway.
I picked up a dozen of the Amprobe AM-47 last year which is basically the same DMM, although it's possible there are minor internal differences. $10ea and they were all new old stock, sealed, and of course the batteries were all in various states of discharge. About half would not power on at all, a few would power on and then reset immediately in Auto mode, and the remaining worked fine for some time before starting to exhibit the classic reset behavior.
Previously I had read about the reset issue so I purposefully left a bunch of them in endless resets for quite some time and did not see any failures.
After ordering a random supply of CR2032 batteries (Sony, Maxell, Energizer), I did determine that it's really hit or miss on these. Some were almost 3.3V out of the package while others were as low as 3.05V. I've also seen some that test at a reasonable voltage but then drop with any load. Even among the name brand manufacturers, many did not have any date codes to properly reference their age.
I kept a few of the DMMs for vehicles, travel bags, various home and work locations, etc. The rest I gave out to friends and family.
Typical power draw is under 1mA, but during startup in Auto it exceeds 7.5mA, which can trigger the reset on weak batteries. Powered off it seems to consume around 1uA.
So, I would be curious if you connected yours up to a power supply set for 3V if it would work correctly? To eliminate any possible battery concern.