1996 Tahoe battery drain

Two months ago I was driving at night with my lights on when I noticed they began to get dimmer. After approximately 15 minutes the power had completely drained from the battery and the vehicle stalled. I replaced the alternator and battery and everything was fine for about a week. Then the problem occurred again. This time I got a alternator with a lifetime warranty from Advanced auto parts and it worked well for about a week until the problem happened once more. This time I took the vehicle to my local Chevy dealer who said that it may have been bad alternators and to put on a AC Delco one. Worked great for about a week or so until the problem happened again. After the alternator is replaced the truck has plenty of power and voltage indicator holds at around 14. Then a week or so later it begins to slowly decrease, until finally it get's so bad that it will drain the battery in one short drive. If anyone has heard of this or has any suggestions I would greatly appreciate it. I have an appointment with the dealer but they said that they are not sure where to even start. Thanks

Check the positive battery cables for corrosion at the battery.
The corrosion will prevent the proper flow of electricity and cause some really wierd problems.