If you have it set to 'always on' it will shut off when you pull the power cord, even if the battery is charged. When the charger is in the port again, my laptop stays on - however, the LED indicator on the front edge of the laptop, (which is white when charging, and orange when about to die), is flashing orange non-stop. If you go to display properties, select the screen saver tab, then click the 'power' button, in the power schemes field is a drop down window, click on it and select 'Rixane Power Scheme', it is a power switching utility that quickly switches between AC and Battery when the power cable/charger is plugged in or unplugged while the laptop is on. I can't tell if it came off and is stuck inside the laptop charger's port or if it fell on the ground somewhere.
Then I noticed that the plastic ring that's usually at the very tip of my charger connector is missing. You should maintain your laptop and this will increase the functional life of your laptop. Like any other machine, laptop requires maintenance. I tried turning it back on and it wouldn't start until I plugged it back into the wall. Normally there is an issue with power supply, but I will explain in detail the reasons for laptop not turning on even when plugged in. As I unplugged the cable, the laptop immediately shut off. I had it plugged into the wall and then unplugged it to relocate. Prior to this afternoon I had no issues with the laptop or its battery. I've seen posts saying that if your laptop only turns on when it is charging, then you need a new battery - but my case might be a little different.
I've had this laptop for about two years.