My S3 started doing the same thing a few months ago, and so did my friend's galaxy. I think my wife's Note 2 is starting to. I suspected the battery was going bad, bought a new one. Same thing. Tried all the settings options to save battery, and turning things off (I never had to do this before, so what's going on????). I tried a factory reset and wiped the cache today, no improvement. Monitored battery use, and screen is at the top 37%, a game I play a lot is next 26%, Android 15, then OS 6% and a few others. Others online have tried a factory reset, wipe cache and have not installed any apps, just the base phone, text, email, and browser use, and they report having the same issue. Perhaps the latest OS version is at fault.
I'm interested to hear the fix. There are tons of threads all over the web on this, so we are not the only ones, and I hope a fix happens soon for all of us. I tried virus and malware removal tools too, no help there. My friend thinks AT&T or samsung (or both) have an engineered "flaw" to time out after a period (about 18 months for me now) to get you to upgrade early (with required 2-year contract agreement) to keep you as a customer. I'm beginning to think he's right.