It would be nice to be notified when a LinkedIn connection decided to dis-connect.
Presently when I notice the number of connections change, I scan through my address book in LI to see who is on Linked in and not a connection. Tedious.
AFAIK there isn't a (native) solution to get notified when someone disconnects from you on LinkedIn.
However, I would also think it's inappropriate. It's like saying:
Furthermore, what use does it have, if that person actively decided no longer to be in touch with you, it's unlikely you can change his mind (or not worth trying)