Hi, I had the same Problem, but I was able to fix it.
- CyanogenMod 10 on a Galaxy S2
- Google account uses 2-Step verification
- Google Mail was syncing but not showing new emails
- Market had no problems
- but same error as posted above
- Disconnected from Google-Account
- Connected again to Google-Account
- Connected to Avast
- anything works, including Mail and Avast
I forgot to test if it is enough to simply disable sync,
wait for a while and enable it again. However, it appeared to me that
the automatic sync must be enabled while you connect to the Avast Account,
so you might want to try this first.