Battery says "plugged in, charging" but the laptop is not charging. It is a refirbished acer aspire that i got a few days ago. It will charge when the laptop is off, but when it is on, the battery will freeze at the percentage it is at until it is shut down.
The implication of this situation is that the charger is supplying just about enough energy to run your computer and therefore does not have any excess to charge the battery while running. I would not worry about this. Worry when the charger won't charge the battery with the computer off.