Are you doing harsh work with these meters or is this some unknown weakness they have?
If I was I would have mentioned it. As I said, my replacement was used twice to measure a simple 5VDC circuit. Between the first and second time - as in, before it was used the second time, it failed. The other meters are also not abused in any way, usually used for low voltage DC circuits and simple tests.
You could try go up to 3.3V for power to see if it's a battery issue. But the defunct ranges seem to point out the mux, as a guess.
I checked and the Brymen 27s has legit 61010 UL certification, so it should not be fragile for ESD.
Unless the plastic shield inadvertently allows arcs between internal nodes on the PCB...
I'm not thinking it's ESD though it could be possible. I noticed this when my meter crapped out after it had a low battery. I ordered a replacement, and my friend said the same thing. I checked my old PM55 which worked last time, and sure enough, same thing. My replacement PM55A showed good voltage on battery, but next time I went to use it, low battery...checked ohms range, sure enough, same fault. Replaced battery with fresh, tested cell, fault still exists.
Not to blame the low battery, but that, and non-harsh use, are the only similarities. But perhaps the zip-up case they come in can generate enough ESD to blow something up?