This is what the support team wrote:
"The "Not enough storage" message means that you don't have enough memory (RAM) to process incremental updates that are small size to download but require some memory to process. As the virus database size grows, also memory requirements are higher. For now, at least 80MB free memory is required.
Besides installing more memory in your computer, I'd recommend to close all running programs and try to start update manually again.
If it doesn't help, download and run the latest full virus database updater (now around 25MB):
http://www.avast.com/eng/updates.html "
I downloaded from the indicated site, ran the downloaded EXE file and now everything finished and my virus db got updated to the latest version and apparently everything runs fine..
Conclusion: disable automatic update, and do a download and install of the new virus db on a regular basis (daily or weekly)
Hope this helps