Classic/Antique Car Repair: 1951 mercury 3-speed overdrive, ford mercury, electrical drain

Question
Ok, so, I know that you know more about the 1960's but it's close to the same thing in this case. I have a 1951 Ford Mercury and we rebuilt it to be all-original. I'm having a problem with the 3-speed overdrive transmission. (6 volt) The overdrive will kick in until it gets hot. (for example) We drive about 15 miles and it will kick in all the way, but then on the way back it won't kick in at all. When we get back in the driveway the battery is drained way down. It's like the generator isn't putting out enough amps. But we've had our generator checked more then once and we've gotten more than one new voltage regulator. My dad is very good at this stuff but he has no idea what is wrong.

Answer
Electrical problems are VERY tricky...
You checked two out of three of the electrical problem triad. Gen/alt---regulator--battery.
Take the battery to your local BIG parts store have them run a check on your battery. IF.. that is not it I would suspect that you have an electrical drain somewhere. Try this... remove NEG(-) battery terminal. Place tester between Battery post and (-) cable. If there is any draw you have a short.
Remove one fuse at a time until the draw is found.
If this did not do it. Then start at the basics .. UNDO and re-tighten EVERY ground screw on the car...Then use a continuity tester to check them. Let me know if this helped.
In the mean time I will search for more specific info for your car