2006 Ford Five Hundred Radio stays on after vehicle is shut off. Runs the battery down

I'm not an expert on this, but radios are supposed to be wired through the fusebox so they turn off when the car is off. It seems like your problem is that maybe the circuit that the fuse runs off is bad, or someone bypassed the fusebox and wired the radio straight to the battery. I would check the fusebox with the car and radio on, pull the fuse that is supposed to control the radio and see if it makes it go off. If it doesn't go off (or if there is no fuse there) then someone has bypassed it. Either way, a local radio shop should be able to fix it pretty easily and it wouldn't cost you as much as replacing you battery all the time. Sorry I couldn't be of more help, but I hope this at least gets you in the right direction. Good Luck!