The fact that it starts at all says that no matter how crook the fuel might be, it still burns. It also says that the ignition is working OK
An engine really needs only compression, spark, & fuel to run & the first two seem OK for now.

It sounds like the engine is running out of fuel, so give it a new filter [you were going to do that anyway, right?] then try again. Have a look at the sight glass on the front of the carb. You should see fuel right up to the dot in the center of the glass.

If necessary, remove the air filter & get someone else to start it while you watch the glass. The fuel level should stay in the middle of the glass when running.

Other hints.
Screw the idle speed up just a little & see if it will keep running at a fast idle. If so, let it warm up before doing much else.
Look down the carb to see if the fuel squirts out of the nozzle when you quickly open the throttle fully [engine off]

Other possibles
Unserviceable fuel pump.
99.9% Out of fuel.[sucking a lot of air]

See if you can get a Gregories workshop manual as these are full of diagnostic hints & troubleshooting procedures. If you can't fix a stocker with one of these, it's because you can't read. They're good books.

It looks like a tidy little unit, & I love the 'speed stripes', so good luck with it.