Precision 7720 - strange issue with battery charging

I have recently started experiencing a strange behavior as it comes to charging of the battery in my Precision 7720. Basically it goes with the following pattern:

- the battery is discharged to some level so I connect the AC charger

- operating system (the same in Ubuntu and Win 10) displays that the battery is charging

- however, the charge level stays on the same percentage (e.g. 35%) and is not going up no matter how long laptop is connected to AC charger

- in BIOS everything is shown as correct: battery is ok, charger is recognized, an indicator displays battery mode as "charging", and still on the same percentage

- now, interesting part, when I reseat the battery (take it out and in for a moment) charging starts working as expected, percentage level goes up while charging

- then it works correctly for some time, and after some period the pattern starts to happen again

What can be the problem? I have run out of ideas? Can it be an issue with the battery itself?