If you are starting from a fully charged battery, you have one of two problems. Either the battery is unable to hold a charge, or you have a small short somewhere that is draining the battery. Suggest this:
Get the battery fully charged and then disconnect it at the negative post. Let it sit for a few days, reconnect it and try it. If you still have the problem, it is the battery. If you don't, there is a small short somewhere. Then the detective work will have to begin...
Forget the regulator - it is not the problem (if you described all the symptoms in total). The regulator keeps the alternator's voltage at a constant voltage for the battery charging. If it is bad, you will either not be charging the battery, or you will have an over voltage condition. This only operates when the engine is running. If you are discharging while not being used, it cannot be the regulator at fault.
Take one of your battery cables loose from the battery, and put a test light betwwen the cable and the battery post. Manke sure everything is turned off, doors shut, etc.. if the light lights up brightly, you have a current draw. Start pulling fuses, if your lucky one of the removed fuses will dim or put out the light. c Then you'll know at least what circut the short is in. This will take less time than letting it sit up disconnected. KD Tools makes a short circut detector for about 30 bucks, that works like a champ...if its in a fused circut. Good luck
Test the battery or substitute a good battery for yours. The diodes in the alternator could be bad. When you check for short circuit/ elec. drain you must disconnect the clock and/or the radio if it always draws current.