I am having a similar problem, after a fresh reflash of the device using the windows flasher, these are the steps I have taken today

used the windows flasher to reflash.
put my old memory card back in (it is an inexpensive micro center 16gb microsd, though the problem continues with or without it after a reflash, though I have noticed that it sometimes wont find it until I remove/reinsert it a few times)

listen to music for ~ hour, continues to work fine until...

connect to an encrypted network (results are the same with unencrypted), when I dont use it (like to browse the web or install apps) it will work for a short while and then shut off, with or without the power cable in (at this point I restarted it and was hoping that this would tell me if that battery is failing, I strongly suspect this is not the case) When I use wifi at all it dies within 5-10 minutes.

Today, after I fully charged it, I got online, installed skype, and when I started it the device said "RECHARGE BATTERY" and the battery icon turned red and it died.

after a restart I tried top, and I have a few "maemo-launcher" processes running at 20-26% usage. even before I started skype or connected to the net.

In the past I used linux to enable R&D mode, I have yet to disable it, my reason being that It was the first thing I did after I bought it, and it never seemed to cause problems (though I have reflashed it since, I am not sure if that is a persistent setting that stays after a reflash).

since I have started typing this it has restarted 6, no, 7 times.

I used to have kismet installed and I know it didnt play well with the wireless, but had not experienced problems like this, I have not installed anything on this device other then skype, and the problems started immediatly after the installation, though I still suspect this is a wireless issue.

The next step I would like to take is to format the internal card, I have seen posts saying that this may fix it, are there directions somewhere? is there a solution to this available? I would be very appreciative of any help.