Power only CHARGES battery in one direction but provides power either direction

So I have a MacBook Pro... I think it's 2010ish. I've noticed that suddenly, the way I've always plugged my power in doesn't actually charge the battery. The battery recognized that it's connected to power but says it's connected but not charging. When I turn the plug around, it sees the power then starts charging. It's really annoying since the direction that will charge makes the cord more in my way and more likely to rip the entire laptop off the desk if it somehow gets pulled (not likely, but still). I would understand if it didn't work at all in one direction, due to the explanation I got here http://superuser.com/questions/111705/why-does-my-magsafe-power-connector-only-w ork-one-way-round (first response by redtuna), but since it kinda works both directions, I'm not sure that applies. My computer is completely updated. In fact.... now that I think about it, it might have started when I updated. Any ideas?

Also... In about an hour of ONLY playing music, my battery went from 96% (at which point it stopped charging so I haven't gotten back to 100% in awhile) to 19%. Any ideas on this either? The power was plugged in the whole time!