What kind of engine? Check fuel flow from tank to carb, HT engine maybe the strainer in the fuel valve inside the tank is plugged, from rust and junk inside tank. You have an inline fuel filter?
Possibly vapor lock and its starving for fuel. Loosen the cap for a test. Push the tickler button for 10 seconds. If thats it, drill a tiny tiny hole through the center of the cap. (needle size) Dont worry it wont spash out if its super tiny. This sounds similar to one of my experiences.