well, here's my 2 cents....

if you jump in your car and crank up the radio, does the sub cut out? Assuming there's nothing wrong with the amp internally, I can't imagine it would overheat very fast. It would take a few minutes even at extremely high output before a thermal issue would show up. I would check the connections again. Make sure things are nice and snug, and not rattling loose when the sub hits. Also, does that sub have a protection overload circuit? If so, it might be the culprit. Can you get your hands on a different speaker (still 4 ohm) and swap out the sub? Eliminate one thing at a time.

Jason