You say the battery is full, but it sounds like it isn't. It is very common for a battery to say it has a charge that it doesn't have when it is going bad. And if it is a replacement and aftermarket battery, that is even more common. Batteries that are dead or dying will often show up as haven't a percentage of a charge that they do not. If that is the case here, the only fix is to replace the battery.
Now if the battery is new or newer, then I would contact where it came from (place purchased or the manufacturer if it came with the laptop) and have them look into replacing it.
If it isn't new, then it just is its time. They don't last forever.