69 Dart GTS 383 4 Speed Completely Original

I just recently acquired a 69 Dart GTS with a 383 4 speed. The car is completely bone stock original. The original owner died in 1976 and the car hasn't been driven since then. The last time it was started was in 1988. There are 43,400 original miles on this car with no rust. It has been kept in a garage and never seen the snow or salt from the harsh PA winters. I got the car running about 3 weeks ago. I had to replace the fuel tank, fuel pump and lines, rebuilt the carb, all new brakes and lines, master cylinder, new alternator, points, plugs, wires, rebuilt radiator, etc. I have put about 500 miles on the car and everything was working pretty much fine until last weekend. As can be expected with a 45 year old car there are issues that will need to be worked out. So last weekend we had the car out and on the way home it started raining so I had the lights, wipers, and defrost on. My lights started to dim and the alternator was showing that it was discharging. I assume that the problem was a voltage regulator so I replaced the original with a cheap made in china deal and it worked for about a day. Now the car is doing the same thing dimming lights and discharging. I am clueless when it comes to electrical issues so I am wondering if the problem is just a cheap part or could there be more underlying electrical issues. Any help would be greatly appreciated.