The SSL certificate I'd been using for this site had been about to expire, so I tried yanking it so I could replace it with something powered by Let's Encrypt (which is backed by the EFF, Mozilla, Automattic, etc…). But, Let's Encrypt doesn't launch until the fall, so the timing wasn't right. In the meantime, some browsers were throwing fits as some of the parts of my site were still trying to load via secure HTTPS connections, while others weren't. Chaos and hilarity ensued. 
So, I just threw some money at the problem to get a shiny new certificate from SSL2Buy to get the site back on the air. I'd been trying to set up a free certificate through StartSSL, but that just didn't work (and Firefox still freaked out with the free certificate).
SSL really needs to be easier if it's going to be used by more folks - especially important, since Firefox is trying to deprecate non-secure HTTP.