I have similar problem on my iPhone 4S,
I think it started to behave like that after update to 6.1.1
6.1.2 didn't help. I'm thinking about getting back to 6.1.0
I can change volume in Settings using slider and sounds is played ok, but when I'm somewhere else it's not working - I can't change the volume.
I can change the volume in while it's attached to headphones.
That's really horrible bug which should be fixed ASAP!
There's another thread on this, and no word from Apple, no solution, and the update wasn't for this. This problem seems to be affecting a small portion of us, small enough that Apple doesn't seem to have ANY concern at all.... If anyone comes up with an answer, I sure would love this annoying problem solved.