Firewall-wise, I only have Windows Firewall (as far as I'm aware) and Ad-Aware is in the allowed list. I noticed that when I try to update Ad-Aware, the app. that's actually trying to connect to the net (the Update Manager) is not the main Ad-Aware.exe program but in fact Ad-AwareAdmin.exe. So I added that to the allowed list, too, but still same problem.

I've attached a screenshot of the error. It pops up immediately after the Update Manager window appears (in fact, it probably happens simultaneously!).