when it dies immediately take fuel cap off and see if it has a vaccum on it, if so you have a vent stopped up. Also like mentioned the rubber lines may be soft and closing up ,Joe
i agree take the fuel cap off and see if the pressure returns. i the tank is having problems venting the fuel pressure will go away.after it sits over night the tank vacume goes away and your good again. i say your looking in the right direction there should still should be fuel pressure even if the carb is vapor locking. also check fuel lines before the pump. check that they are not getting heated up from exhaust. if it vapor locks before the pump you wont have fuel pressure either.