Why the computer is turned off?

When connected to the laptop is charging, it starts to beep until shutdown.

Check the charge on the subject of voltage and current under load - it is likely that the battery is faulty and just does not hold the load.

Logic with memory can be implemented in different ways, and often made so if charging is disabled, are powered from the battery.
If the charger is connected - powered charging, plus a rechargeable battery, such implementation in the memory when connecting to go double duty - you need to feed the laptop and charge the battery, and if she can't do the voltage drops, and maybe a trip. Or voltage instability in the network, then even the normal charging is possible, this situation.

Although most of the laptop - when charging the battery is not disconnected, but occasionally it happens and this implementation.

When you turn off the laptop charging properly?
In General, start with the memory diagnostic.

PS - an interesting feature in screenshots When connected to a memory speed of discharge of the battery three times.
You've got to understand that these data are not always accurate, but worth checking.

it was similar with non-native charging at some top-end laptop. try to change\\to contact the service center.

It's certainly curious, Yes... But I advise you not to risk the laptop and take it to a service center, just normal... And let them think, and then you run the risk... If you say what is happening without connecting this charging, the problem is obviously in the laptop itself... some trouble there. Good luck