My first thought was that the engine's (therefore alternator) ground
connection to the car's body is suspect. That would explain the battery
rundown during driving BUT, if were so, then the starter wouldn't work.
So much for that idea.
Either the alternator isn't charging or there's a serious current drain.
The alternator has been replaced a couple of times - with a Bosch
alternator? Or brand X junk?
You can sequentially remove each fuse and put an ohm meter or 12v test
light on its circuit to determine if there's a drain when the engine is
shut off. There should be no current flowing other than in the clock's
If the car was ever wrecked the crash site should be checked for a
pinched or bare wire that may be shorting and draining the battery.
Another suspect is the power antenna; its power supply line can be
unplugged as a test.
A dealer will be only too happy to take your money, especially for
investigating something so open ended. This isn't rocket science but a
process of elimination.
If you can't find the problem, take it to an auto electric shop.