I never let the batteries get too low, I charge them at around 3.6v, and they have never been below that. Doing a reset does always work. Like I mentioned before, someone claims this model has a rechargeable button battery on the pcb, which can act up if not used enough. Supposedly the button cell operates some of the circuits, not just memory. It could be either battery.
Another potential issue I encountered with my Tecsun PL-398, which uses 3 AA's. When I moved the radio one day, just holding it, it turned off after giving me a 'low battery' warning. The batteries were new. It happened twice.
It was the battery moving around inside the case, just enough to cut out the power for a few milliseconds or so. I could tell that the battery was moving slightly, because when I opened the compartment I could wiggle the AA slightly. So I tried a shim.
I cut a shim out of some plastic (from a plastic bottle which had flat sides) and shoved the shim against the battery in the battery compartment. The compartment cover still closes OK. The shim keeps the battery from moving at all. I haven't had any problems like that with my Tecsun since.
It might be your rechargeable is moving around in the compartment just enough to cut out..... Or not.... It's still worth trying, though, if you still have this issue. A plastic shim would be cheap enough to make, and it would either stop the problem or at least help you zero in on the cause of the problem if the shim doesn't help at all.
I've used shims in other radios where batteries moved around. In my Sangean PR-D5 battery movement caused crackles in reception when I moved the radio. The shim stopped that. My DX-375 would need the power button pressed a couple times to turn on when the batteries got a bit low. The shim solved that, too.
