I have run into this as well on specific sites that require a secure connection. I’m running Mountain Lion (10.8.4) on a MacBook Pro. Specifically, I’ve narrowed the problem down to have the Scan secured connections checked within Web Shield. With Scan secured connections checked, I can’t access Dropbox, Kindle, or Mac App Store updates. There may be more but those are the ones I’ve seen. I’ve tried exclusions, but they don’t make any difference. I’m not sure when this started as avast! updates automatically. So for now, I’ll leave Scan secured connections unchecked and hope for a quick fix.

Bob