I haven't heard of a characteristic coil problem with that engine, but it has such an appalling reputation for carburetor problems that perhaps the subject has never come up before.
I suggest you check the flow rate of fuel through the fuel line and fuel filter by removing the float bowl and checking how long it takes to fill a cup under the carburetor. From your description, the problem may be lean misfire. Restrictions in the fuel flow rate normally allow the engine to start properly, but the flow of fuel into the carburetor float bowl is then insufficient to replace what is being used, so the mixture gradually becomes leaner until the engine misfires, and possibly stops.
