I got a note from them...
"You are, no doubt, a person who (like me) uses Firefox browser. This is an old problem, but it is exacerbated with the newest version of Firefox and a rather "unique" bedfellow they have developed in Google.
Our host company is working to rectify the problem (which has just reared its head today), but essentially it revolves around "shared" hosting accounts. Our websites are on the same servers as some other companies. The secure server is an entirely different entity, but if Google (they're the ones that spider the websites/servers) perceives anything at all in a page or scripting of ANYONE'S website on a shared server, they brand everyone as an "attack site." What is really stupid about this is that if you go to our site using Microsoft Internet Explorer, there's no problem whatsoever. It's kind of like having a criminal living on your street and thus the entire neighborhood is branded as a criminal. Only in this case, if I'm to believe our host, the "crime" is pretty benign. Something to do with one of their other customers having some sort of live customer chat/support. I'm sure the host will have no choice other than to shut down that website if not the application so the rest of us can get back to business as usual. But before that can happen, the host must prove to Google that it's "clean." In the meantime, the 85+ % of people out there using Microsoft Internet Explorer have no problems at all.
Hopefully it will all be resolved in a day or so...that's what our host says. In the meantime, you can call and give the CC information if you wish, or just use a browser other than Firefox.
Sorry for the inconvenience."
I am using Firefox, so maybe he's right...