Well. I solved my own problem. My server was running too slow. I guess the feature that parses URL’s was timing out. I installed the APC PHP Accelerator on my server, which DRAMATICALLY cut down on the execution time for PHP scripts.
https://howtounix.info/howto/php-accelerator-apc-on-linux
Suddenly, the URL’s were parsed.
WordPress, you might want to update the code to detect server time-outs when parsing URL’s.
Hope this helps others.