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Firstly, follow Patrick's advice and determine if you have the proper battery cables. I am not referring to length here. I'm talking about the correct gauge for a six volt system. Ill-informed owners often just buy 12 volt cables (to the starter and possibly as a ground) at the their local auto parts store and think they are sufficient. They are not! They are too thin and will degrade the current, causing your symptoms. Either take a photo of your cables and post it here or compare what's in your Model A to your modern car battery cables. If the same diameter, they are the wrong ones. You can only get the proper battery-to-starter cable from a Model A parts dealer. The local auto parts store will not have these.
Also as suggested, make sure the ground strap anchor point on the center crossmember is shiny bare metal. You can't expect a good ground if paint or rust is between the ground strap end and the crossmember. This area must be surgically clean in order to achieve the strong ground so necessary in a six volt system like ours.
Anyway, check these items first before going deeper into the problem.
Marshall