Ok, this has happened twice now, so I figure I should try to fix it...

So I'm sitting in my car with the engine running but parked for maybe an hour. After this extended period of time, I notice that the tachometer is starting to fall slightly, but not too bad (maybe 500 rpm). Of course, the idle is a bit rougher (as if its about to stall) but again, not too bad. The tachometer continues to fall and then all of the sudden the car stalls. The weird part is, is that the car won't start - it won't even turn over. I jumped it the first time, but I just left it in the parking lot tonight. At first I was thinking maybe the battery was dying, but why would the battery be drained when the car was running? So maybe the alternator?

Any ideas on how to fix this would be appreciated because I'm getting tired of this...

Thank you in advance.
Peter
1988 300E
1988 420SEL