My Aspire 5551 battery works perfectly, still has a 2+ hour battery life!
However the laptop only charges when it isn't running!
I originally thought that it was a problem with my power cable, but I have just replaced it (with another official one) and the problem still persists! Could it be the DC Jack?
I'm going to take a stab and say that it is not the DC jack.
Your charger is putting out just enough to run your computer, leaving no excess for battery charging.
No need to worry here (yet).