I think I had the same problem, despite only have 1 or 2 favourites.
What it really means is that you have too many secret bases scanned already. Delete a few and it should let you scan again.
Also, I'm not entirely sure if the new base QR code will override the old one if they're in the same place, i.e. you already scanned a secret base in the Secret Islet, I'm not sure if it'll let you scan another for the same place and override the old one or just tell you that you cannot scan, so check where the location of the secret base is that you want to scan, and see if you already have a someone else's base there.