Ok, I think I know what's going on. I fired up a VM I have, running xp x64 + Avast 8. Avast updated normally to v 140212. Then I installed avast 9 over avast 8 and rebooted. After rebooting, avast updated to v 140409-3 instead of today's update.
So, it seems that for some reason, avast won't update to anything newer than 140409-3, that's why it doesn't update if you have a newer version (installed via the offline updater, for example).
Of course, trying to update gives the same result: It's already up to date (which it isn't!)
THIS IS DEFINITELY an issue with the v9 update servers.