For $120, hard to knock it. Was glad I finally was able to run one.
I turned off both the Extech and CEM's phonating function. I then left the meters on for 1 minute. I then pressed the pressed the crap out of the BL buttons. Both meters did the same thing, no effect. So yes, it appears the problem is tied to the beeper.
With yours having a CJ part and higher SN, I suspect it will run to a lower voltage. I did not check mine but that new Extech will run the battery into the ground before it stops working.