I had this very same issue with my Shelby about 15 years ago. The alternator charged fine and the car started fine as long as I didn't let it sit more than a day or so without running. I took the battery out to have it tested and noticed a rather large spark disconnecting it which means there is a load on the battery....on a 30 year old car that has not memory items or loads when the car is off. After some thinking I figured it had to be a diode in the alternator. Took it off, took it apart, and tested all the diodes only to find a bad one in the tri-diode pack. A few dollars later the problem was fixed.
1966 Shelby G.T.350H #1781
1966 Mustang Fastback restomod project
1966 Mustang Coupe restomod project (this one will get over 30 mpg!!)
I'm a car guy, a computer is a tool not a pastime!