Starts, runs quits acts like short on gas
fa50 starts and runs good then sometimes acts like it runs out of gas, other times it stays running. When it quits if you wait 15 min it usually starts and runs again
It sounds to me like you are having fuel issues:-) clean your carburetor and the fuel bowl. It could be that the needle valve is stuck. Also make sure that your tank is nice and clean on the inside without any debris. and that your fuel line is not kinked. There is more about it on 30 years without using It also includes a link to the manual and parts list I posted on my fileserver. do feel free to download it. It will help you getting your moped back on the road soon. Good Luck
On those itty bitty carbs the mopeds use, a in-line clear fuel filter is mandatory, also if you are running the standard E-10 (Ethanol blended) fuel,,, run Stabil in it. And keep the tank FULL never let it have much air in the tank when left un-operated for more than a couple weeks. If you have to store it for more than a month or two find a farm or marine pump that will sell you a can of Ethanol free fuel add Stabil turn the gas off and let it idle till it stops.
Your symptom is typical of a fouled carb , +1 on pulling the float bowl and giving it a dose of spray carb cleaner..
Bet it's either something in your tank resisting gas flow.because suction or vacuum pulls all debris together inside fuel filter.When you stop and wait.the suction stops releasing debris and letting gas to flow by enough to do it all over again.check tank petcock fuel lines.and float bowl in your carb,