Hi Steve,
Your setup with broadband and telephone using the same line is quite common in many places and should not be able to affect your Beocom 1401 when it comes to its storage.
The numbers are stored in a non-volatile memory and should be kept regardless of the phone being connected to mains or not. No batteries - no nothing. If it looses its memory my conclusion would be that the phone is defective.
I have never heard of this kind of problem before though with Beocom 1401.
Br,
Burnix