It almost sounds like a fuel system problem, especially if it seems to consistantly have a problem so many minutes into a flight. Things I would check for are a split in the clunk line which allows the engine to suck air after the fuel level drops to a certain point; clunk fell off or is touching the back of the fuel tank; vent tube touching the top of the fuel tank. If the plane has a fueling device/valve it would be highly suspect. If the diaphram(sp) has been vented make sure the tubing is not melted from touching a cylinder.
It might be worth mounting it on the bench and running it. If it shows no signs of a problem after 6 minutes then the problem is in the airplane (airflow, fuel system, etc)
Len