With a car that age chances are a previous owner had fitted an aftermarket HU at some stage. They most likely connected the switched power to the perm live (as Audi wire them back to front) instead of just swapping them over. So you now have no switched live going to the HU, and have to switch on/off manually.
Just pull the HU and take a pic of the black ISO connector on the back so we can see what they've done, should be a really easy fix. The worst part is pulling the HU, get the right removal keys and be very gentle. Don't pull on the keys, remove the glovebox and push the unit out from behind. The spring clips that hold it in are very fragile and you can easily end up with the HU wedged in there.
There is a chance that when they put the car back to stock to sell it they bought a replacement HU off ebay or the like, and it's the newer style CANBUS operated version. This won't use a switched live, but uses the CANBUS to tell the HU when the keys are in/out. Unfortunately if this is the case there is no way round it, as your car is not a CANBUS equipped vehicle. Does the HU switch off after an hour?
