Adding the correct exception for Avira is a pain. I will add the procedure for information purposes only. The easier way is definitely disabling webguard while downloading.
If you really want to, what you need to do is the follwoing:
1. Close all open programs that might try to access the internet on their own, especially Firefox etc. Also close the GOG Downloader.
2. Open Avira and go to the online protection part (Online Schutz) and select Webguard. There is a "last checked URL" (Letzte überprüfte URL:).
3. Start GOG Downloader and switch back to Avira, checking to see if the last checked url changes. Mine e.g. said
http://wpc.11df.edgecastcdn.net/something/something/witcher2/part_something. This is the download URL that is actually blocked and also the reason why simply unblocking www.witcher.com or www.gog.com will not help.
4. Copy the URL from the last checked URL location (select with mouse and cut/paste as usual)
5. Still in the same Avira Web Guard window hit the upper right configuration button
6. Go to "Web Guard" and Search (Suche), then select "Exceptions" (Ausnahme).
7. I strongly suggest to read the help at this point
8. Paste the copied URL in the appropriate entry box where URLs can be exempt (it is the lower one, not the upper one). But make sure to cut some of it. E.g. the .../witcher2/part_1_something should be cut down to .../witcher2/* (with an * at the end). Else you would only unblock part 1 of the download and the other 4 parts would get blocked again. Hit the "Add" (Hinzufügen) button, then ok and you are done.
9. Check the GOG downloader, mine started downloading within a minute. Else try restarting it.
Best regards
Shawk