Intermittent 'Battery not charging'

The charging is not throttled per se, but the power is provided first to run the computer, and second to charge the battery. But not enough is provided apparently. This reminds me of liquid damaged boards with partially corroded lines between charging chip and battery. The "bottle neck" would prevent the laptop from replenishing the battery during normal use, but would otherwise charge when turned off - but slowly.

So either you have corrosion on this line, from previous / old liquid damage; or the board was previously replaced from Apple by a refurb and those lines were indeed corroded; or the components on that line and/or charging chip are compromised and not working fully. Or the charger is failing somehow.

It should be easy to troubleshoot.

1/ I would start by downloading Coconut battery and monitoring the charging process and charging wattage during different types of loads.

You can also see the charging from "Apple">About This Mac>Overview>System Report>Power>AC Charger Information>Wattage.

2/ If you feel something is not right with the battery or charger, you can try a different preferably known good (not necessarily new) charger and/or battery (one thing at a time). May be even the MagSafe DC-in board.

3/ Third step would be to remove the bottom cover, disconnect the battery, and look around for traces of corrosion. Specially slightly north of where the battery connects.

4/ If nothing jumps out at this point, you would either have to send it to someone who can perform board level repairs, or whip out a multimeter, schematics, a board view, and start troubleshooting. Then if you do find something wrong, you'd have to be able to microsolder replacement parts.

Final note: this model is highly prone to GPU failure. Take it into consideration before spending big bucks to repair it. It's a shame since with an SSD and 16GB of RAM it still performs outstandingly.