I had the same problem but more severe. It turned out that it was the gas tank itself. Since you need to replace the filler neck. Check the inside out. It may appear outwardly fine but espicially if it is the orginal tank it could be rusty. I would run my car and then it would die or simply not start until I got the lines cleared. If this is the case and a new tank is to much I would suggest a gas tank sealant. Used it in my 49 and have had no problems with.

1941 Chevy Series AL 3/4-Ton Pickup Truck and 1949 Chevy 2-door Fleetline Delux Sedan