I would also try a second regulator. My wife's 66 mustang had the same problem a while back and I went through the same thing. The first thing I changed was the regulator but that didn't help so I had the alternator checked and it was bad. I put the new alternator in and it still would not hold a charge. What had happened was the bad alternator had fried the new regulator. I put in a second regulator and it's been fine so far.
I also went around and cleaned up all the ground connections while I was at it anyway.