If a simple reboot of the robot (power off, wait 10 seconds, power on) won't make it work, and the nano program is truly wiped out and has to be reflashed, then that sure sounds like a bad nano. Under normal circumstances nanos won't lose their program on a regular basis. Yes, a static discharge can cause that every now and then, but even that's not super common and it certainly wouldn't happen on every run.
We do get batches of nanos every now and then from our suppliers that have various issues and have to go through the return process. It's just something that happens if you buy inexpensive items from china. We test every nano before we ship it.
The battery could be an issue too, it might have a very aggressive protection circuit that cuts power as soon as more than a couple of motors power up. However, I've never seen that wipe out the program on the nano. If that was the only issue you'd be able to get it to work a few more seconds by just rebooting the power switch on the robot.
Ok I just looked up the battery and it is rated for 10 amps continuous discharge so it should be fine, the robot really doesn't draw much more than 3A and even that is only for short bursts. However, if you bought them from someplace like Aliexpress it might be a counterfeit panasonic and then all bets are off.