I've got an early 2011 13" MBP and just recently I've had the odd shutdown. I'll just be doing something, today I was starting to watch a Youtube video, and the MBP just dies. It was being charged so it was nothing to do with the battery. I press the power button to switch it on but nothing happens for about 5 seconds then it switches on and boots up. My Safari window is still open with all my old tabs. So is my MBP about to die?
I have the same model and have had the occasional freezes for a couple of month now. I suspect a logic board failure. At times even the USB ports don't work. At first I suspected the SSD to be faulty but still happened after clean install on a different SSD. I'd advice you to backup your data asap.