Why has my GSIII's battery life dropped from 50-60 hours to 16 hours?
Cell standby being high means you have a really weak signal wherever your phone was.  The phone cranks its radio up to maximum power to try to maintain a usable signal.

There are several ways to stop it - none of them ideal:


Put the phone somewhere with a better signal (near a window maybe)
Put it in airplane mode to turn off the radio (but you won't be able to get phone calls/texts)
Switch to a carrier that has a better signal near your home/workplace


As for why it's doing it now, it could be that you're leaving the phone in a different place in your house most of the time, or weather is affecting the signal strength, or sprint is extra crummy in your area lately.