This has happened to both me and a friend who also has an A4. Try replacing the main fuel filter. It is in a canister usually adjacent to the fuel shut off (usually a Fram).

I found that the filter needs to be changed at the begining of the season and monthly thereafter. I keep a minimum of 3 aboard as I once used them all due to bad fuel.

I have also added a see through in line filter after the main filter. Got it at an auto parts store. It is a see through chamber with a mesh filter. It is a good add on.

You probably also want to try to pump some of the fuel off the bottom of the tank into a clear container. Let it sit for a bit and see what it looks like.

Good luck