Default [Q] Phone will randomly turn off and have low battery when I reboot

I'm on my 2nd S3 as my first one died of a board failure a couple of weeks back so I had to trade it for a refurb. This one I've got has given me some problems. The biggest one is the phone will randomly turn off without warning and won't turn on again without a battery pull. Sometimes but not always, the battery will just drop to nearly dead. The phone is currently running CM11 but I don't believe that's the problem because my other one had CM11 also and it gave me no problems. Does anybody have any ideas why this is happening?

EDIT: I switched batteries thinking it was the battery first but it still does it with a new battery