Have you tried to make a reservation without logging in and then add the membership number later? It might have something to do with your account AWD, dates, or maybe IP address? I tried to book different dates with different car types, with or without login at CPH, they all comes with unlimited miles.
You can also try to use a VPN and search again, just to see if that makes any difference.
Or you can use something like Priceline and book the reservation with your Avis Wizard number.