Car: Audi A8, 1997

Problem: after removing key from ignition for more than 2 seconds the radio demands SAFE code.

I have tried to supply the radio with permanent power from another fuse which have constant power (cigarette lighter, alarm system etc.). If I do, the radio "remembers" the SAFE code and I don't have to enter it every time.
But, of course another problem arises: if the radio have constant power the remote unlocking function on the key does not work. The central lock system works if I mechanically stick the key in the lock.

At the moment I have to choose between entering SAFE code every time with the remote unlocking function working, and not entering SAFE code every time but being forced to open the car mechanically.

Anyone have a suggestion for a solution to my dilemma?