I have a 4S, 1yr 2mos old, with IOS 6.0.1 (10A523). This problem just started for me a week or so ago, quite some time after my upgrade to 6.0.1 (so I don't think that's it); somehow I don't think that upgrading to 6.1.1 will help so I'll hold off, because any software upgrade has its risks.
I just did a very thorough cleaning using, in this order: soft (paint) brush, compressed air, soft toothbrush (gently, to be sure not to damage delicate contacts), compressed air, tuner cleaner (my miracle worker), more compressed air. Examination at each stage using a 60x microscope, until everything was pristine and shiny.
Nuttin.
Next, I tried turning off notifications, per lorddisick's suggestion. I turned off many more notifications than I had before the problem (no change). Then I turned off more, including some I thought suspect (so I wanted to turn them off individually). Nuttin.
I take VERY good care of my phone, using a protective gel case, plus a hip case when necessary. It never gets wet, and I keep it out of dirty environments. Any "shocks" (drops) were minimal (tabletop, not floor), and few between.
The battery is good. I've taken proper care, using recommended conditionning, charging procedures, etc. (there may have been some degradation, i.e. quicker discharge, since the last iOS upgrade, but nothing like what's being reported).
I've tried turing off while plugged in, and not.
Having exhausted everything I've seen here (aside from the wiping and upgrade, which I'll save as a last resort), I thought I'd post my situation for others before I move onto other forums. I wish you/us all luck, and hope to see a solution which works for me soon; I'll certainly come back here and post if I find one!
Salutations,
-MontrealPaul