Fuel delivery problem with tecumseh engine.

Riding lawn mower.  Runs strong, then dies.  See-through fuel filter is dry.
 
So:
 
I've checked the tank. It is not sealed or in a vacuum, so the fuel should flow freely.
 
The tank is above the carb, so the fuel should flow freely.
 
The fuel tank hose stub is clear, so the fuel should flow freely.
 
New fuel hose and filter, from tank to carb, so the fuel should flow freely.
 
Checked the hose for blockage anyway, even though it is new.  All clear.  I can even look through it, all clear, so the fuel should flow freely.
 
New carb, but checked the float and pin.  There is actually a bit of fuel in the bowl, but the pin and the float are free, and there is no fuel inside the float (which would just give me too much fuel, just sayin').
 
The shut-off solenoid is free and works great.  Tested, and can hear it activate.
 
So, if there is no vacuum and/or kinks in the line (1/4" ID fuel line), and the carb is new and free, and the tank is elevated (with cap loose), Why won't the fuel flow freely?  I take everything apart, fuel flows, put it back together, and the thing runs for a lap or two, then it dies with a "dry" filter.  What am I missing?  It can't be clogged jets, 'cause it runs all the fuel out.  Is there some type of back-pressure that could interfere with fuel delivery?  Maybe the heat of the engine evaporating fuel in the line creates pressure?  I can't figure this out.
 
Any suggestions would be appreciated.