You might want to try Firefox.

Thanks, Mike. Firefox is how I was able to make my post. But Safari is my main browser and worked with this website up until a few days ago. I thought MM might want to know about the problem.

Did you fill out a support ticket? You gotta let them know.

Never did one of those.  Where are they? 

Right in the bar at the top of the page: "Submit a request"

Is there a Safari update available independent of an OS upgrade?

Changing security standards may make this an issue that will not be fixed without a browser update.

Just for kicks, I booted from my other drive running El Cap and Safari 9.3. Couldn't get in. Also couldn't access many Apple sites and download pages.

I upgraded to Safari 10.1.2.6 in the App Store and full connectivity was restored.

I normally use Chrome because it is so much faster in my day job.

Thanks, Mike H and R.   I suspected that might be the problem.  Trouble is, I can't update Safari on 10.8.5, and I can't update 10.8.5  yet because...etc. So I will just have to use Firefox for this site.

OK, I looked ti up. The minimum requirement for Safari 10 (currently 10.1.2.6)  is OS X Yosemite 10.10.5, and later.

Thanks for confirming that Mike.  Yes, I am stuck until I update, but that day is coming!