Menu clicks don't change page

A new problem has suddenly arisen on my previously working site. You can visit the site at http://www.eeb.cornell.edu/igert.

Selecting an item from the menu very often doesn’t result in a new page appearing. The URL in the location bar changes as expected, but the page remains unchanged, that is, the page that appears in the browser window is not the page at the URL that appears in the location field. Also, the menu item that is highlighted corresponds with the page that actually appears, even if the URL in the location bar is for a different page.

If you click on the refresh button, the correct page appears. If you wait for 60 seconds and click the menu item again, the correct page appears.

Sometimes I can go through all the menus without a problem, but eventually the failure will appear, and after that, it appears very frequently.

The Apache log indicates that it has served the correct page, even when the correct page does not appear in the browser.

Occasionally the mobile theme will appear when accessing the site from a desktop computer.

It sounds like some sort of corrupted cache, but I do not use any caching plugins.

I have other WordPress sites running on this server, and none of the other ones show this problem.

The menu is a custom menu. The web server is Apache. I have restarted Apache and restarted the server, to no avail.

No doubt the solution will become apparent to me as soon as I click the post button.