Frank,
Check the fuel pump. It might not be working properly and needs a little extra help from gravity. Sounds like you are having the problem when the fuel level in the tank gets to about the same level as the carb and gravity stops helping to feed the pump. This would happen if the fuel pump is getting 'weak' and doesn't have enough suction to pull enough fuel from the tank and pump it up to the carb without the extra help from the difference in the fuel level in the tank and the carb bowl. Could happen!!!
'52 Ted