It sounds slightly strange but I know that the phone doesn't shut down at a particular percentage. The not very technical way to think about it is that the phone shuts down when it doesn't think the battery can maintain the current level of drain for more than 2 or 3 more minutes.
It does this to protect the battery from running completely flat.
The phone will only turn on at 5% charge; so if the phone turned off with more than 5% charge it can usually be turned back on again right away.
My suggestion is that the phone should be drained completely to the bottom, and the fully charged. Then doing a hard reset og the phone by holding the home button and power button until the handset restarts; and then completely draining and charging one more time.
If this doesn't help; I'm sorry but I'd be out of ideas.
Make sure that aplications like "iPlayer" and "Skype" are closed when not needed as these are allowed to run in the background and consume battery. Other than these tips; I guess the battery could be giving up.
Unusual for a young device like the 4S though.
Some people go to the exrtreme of wiping the phone completely and restoring from backup; or just wiping andd starting over and have reported mixed results; but some suggesting that it has solved battery issues before.
I've only had a battery issue once on my 4 and 4S; don't know what caused it and rebooting the phone seemed to solve it.
I've only ever had my phone turn off at 6% on me twice; both times I was just opening an app like Angry birds