I’ve just purchased a new a3 Sportback Black Edition - which is suffering the same issue here. Stored radio favourites stay for a day max then disappear and have to be re-entered.
i have talked to Audi connect services and they have given a number of different replies from “this should not be happening” through to mmi soft reset instructions through to suggesting it may be the strength of the LTE connection to the vehicle.
I read on a US forum that when the car is switched off it sends a data update to the cloud which includes radio favourites and if for any reason this data has an interruption then the radio favourites will not be stored at the next start up.
I have booked the car into a local dealers for a software investigation - but genuinely wondering if this is worth it - given the various comments on this thread already.