Lumina Electrical Issues

This may sound weird, but, everytime I turn off the car, the battery seems to NOT be connected. I get no lights, and my radio stations reset to am everytime. What is causing this? Any ideas on how to fix?

does the car start back up when it does this?

Yes, it does it EVERYTIME, and Starts everytime??

you may have a burnt fuse for the radio memory. What year is your car?