Same thing happening here.  I thought the original battery was dead (would go from 1/2 to very low red level out of nowhere).  Since then I have tried: New battery, new phone #1, new SD card, new SIM card, new phone #2.  I am now on phone #3 and the problem is still happening.  Stays on for short amount of time, then turns itself off - no consistent time frame or app.  I have to pull the battery or plug it in to power it back on.  When the phone remains plugged into a charger, it stays on.

Verizon rep KellySM_VZW, why would it work when plugged in if it was an app issue??  It should behave the same.