Interesting problem, some scenarios I would explore:
1. Check the battery by putting a decent load on it before reconnecting to be sure it is discharged. If it is I would think about the possibility that the charging system is not actually working (especially since you mentioned a new alternator). What may be happening is that you are running on the battery and at the end of the day there is not enough to start it again. Although though you did mention that it starts if you try to start it right after turning it off, that might mitigate against this scenario.
2. Do you have an alarm system or something that must be reset when the battery is disconnected or discharged?
You could do a Google search on this, with enough patience I have found lots of this type obscure problems/resolutions for my wife's BMW. Good Luck!
