Since I downloaded the new adaware I also got the connection error.
I knew I had a problem recently when my google searches were being redirected. I downloaded the anniversay edition. From the start I could not connect through update either within the program or start menu.
When I tried to download manually from lavasoft site, I was blocked from doing that as a "bad link."
I didn't connect my problems with google searching and downloading adaware updates until today.
I downloaded the program Malwarebytes, scanned and deleted the items it found. I rebooted and I was instantly able to update from adaware program. I also checked the definition download page and am able to download that as well.
So for me it was not the software update that killed the connection, it was some bad stuff on my computer.
I hope my experience will help some of you who have experienced the connection issues.