Yeah, that's what I was afraid of. A lot of modern antivirus software essentially hijacks secure connections. They insert themselves between you and the website so they can decrypt the data flowing back and forth (or, in jargon terms, they MITM HTTPS connections). This is likely what's responsible for the intermittent issues, and there's not really a whole lot we can do about that on our end.
There might be literally nothing you can do on your end if it's between the antivirus and some cache service in the middle somewhere. I'll update the thread if I see it anywhere else, maybe some sort of pattern will emerge. Or I'll update something and it'll mysteriously go away, who knows.