If the battery is extremely low it could just be powering off due to low battery. If the AC adapter isn't supplying enough juice to charge it while also powering it since you are using it, it could be causing the phone to still draw battery.

Are you using the adapter that came with the phone? It should have enough power to charge and allow usage. If you want you could try finding another charger that supplies more current. I think the one that comes with it supplies .7 amps and the one I use for mine supplies 1 amp. The higher the amps the more capable the charger is to charge battery while you are using the phone

 

I use the stock charger and while the battery is in the red and use the phone without issue. I think I did this one time even after the phone powered itself down due to low battery.

 

Adding to this, .7 is enough to keep the phone awake usually and provide a little extra charge, versus 1 which charges it from zero to 100 in 2 hours. At least that's the case for me. So it could be that the adapter that came with yours, skullzy, is providing insufficient charge to keep the phone alive and charge it at the same time.