Which beta version are you talking about? There were technically 6 releases of iOS 7 while in beta before it hit GM (though one was a security fix).
I am running the latest version.
I have had this happen on iOS 6 couple of times lately. I assumed it was because the display indication of 10% was wrong or couldn't be updated due to lack of battery power!
The phone will automatically shut down when a certain minimum voltage threshold is reached. This is to protect the battery from damage.
good info, zorinlynx.
My 4S would do this at around 20% sometimes (OS6)... yeah, always seemed to do it when trying to view a vid or similar... Once it died, I'd let it sit for a minute or two, and then turn it back on, and it would be fine.
I did get a replacement a week or so ago (for that and another screen issue), and so far no issues with the new phone.
Recalibrate your battery.