When a quick release slips, usually the wheel slips forward in the dropouts because that's the direction the chain is pulling.

Forgive me for asking what might be a silly question... How are you tightening the quick release? You're using the lever and not just screwing it down, right? And when using the lever, it should be kinda tough to close; tough enough that the lever would leave an imprint on your palm. If it doesn't, release the lever, screw it in a little tighter, and try again.