My Xbox 360 controller keeps shutting off?

I've been on a video game bender for a couple of weeks now. During this time, everything was fine--my controller worked normally. I changed the batteries a couple of times, and my controller was working normally. Then, all of a sudden a couple of days ago it started shutting off randomly. The lights would blink diagonally, like the batteries were dead, and I would change them out for fresh batteries and it would still do it. I'm literally sitting, like, five feet from my Xbox, the pack is securely in, and it shuts off every five seconds no matter the batteries, the connection, or the pack. I read somewhere that I needed to take the batteries out of the pack to clean and re-position the metal prongs. After doing this, it still didn't change anything.

P.S. I notice that one of my batteries sort of rattles around on the plus side of my pack, while the other side it's really hard to remove the battery. I don't know if this is relevant at all, but I thought I'd mention it.