I inherited my 4s from my son when he upgraded to a 5. He said "the battery has never worked right".
What I discovered was that it was extremely sensitive to the charger: only certain chargers and certain charging cables would work, and then, only about 70% of the time (have to plug and replug those that it would accept, until it accepted them). It had nothing to do with cleaning the connector, hard-rebooting, or other simple solutions.
It's like there's a circuit inside that determines if it's going to charge from whatever power is being applied, and rejecting most everything. Just too sensitive.
Then, it got so sensitive, that only 1 in 50 attempts to charge would work (allow charging), then it would not charge with anything. This ramp down happened within a day.
I found if I powered-down fully, I could re-charge the battery... but it doesn't stay charged all day.Hoping that the problem was now the battery itself, I replaced the battery. The first replacement was fully drained upon arrival, and would cycle through a blank screen and the apple logo... which many say is a sign of a bad replacement... so I replaced it again.
The second replacement had a 50% charge upon arrival... but, like the original, will only charge if I power-down fully.
So, I figure there is some circuit that gives the "go" or "no go" to incoming power, and that circuit was always out of spec, but is now totally fried, and the only way to allow charging (and only at a trickle) is to bypass the circuit by powering down.
Does anybody know if there is a fix?