1999 VW Cabrio keeps dying but is fine after sitting for an hour. Mechanic is baffled.

My 1999 VW Cabrio dies on a regular basis.  Almost exactly an hour later, it will start right up no problem.  It dies pretty randomly, but always when I'm going slowly, under 25 MPH.  Often it happens when I'm going up a slight-to-moderate incline.  Today for the first time, it died while I was sitting at a red light.  It used to die maybe once every few months, but it's happening more and more lately.  This week - twice.  In the last couple months, 6-7 times.  My (non-VW-specific) mechanic was baffled.  I think the oddest thing is that it will be dead for almost exactly an hour every time, like clockwork.  What could the problem be?  It's not the battery, starter, transmission, belts, or hoses.  It's not overheating.