Briefly, we configured our web server to respond correctly (i.e. with HTTP response code 200 and a list of supported HTTP verbs) to all OPTIONS requests. Excel seems to make a bunch of these requests when you open a .xls document from your browser, and gets confused if you don't reply as it expects.
The technical details are at
When Tomcat, HTTPS, and Excel collide, and there's no point replicating them here. No idea why Done_Fishin thought he had to "log in"; you don't have to log in to view this simple HTML page. We are not spammers or advertisers; we just have a solution to this problem we are trying to share.