Figured it out--I recently added a script to stop other websites from hotlinking the game file. However, I accidentally blocked blank referers too, and some firewalls strip all referers from HTTP requests.
Why hotlinking the game file is a problem for you? Personally I don't like the websites that used hot links to the JARs because it is silly (it does not work, my game requires several JARs and some native libraries) but hotlinking the JNLP file is not a problem. Maybe you'd like people to get to your website to launch your game.
I'm making a tool that allows users to create games and share them on the website. The .jnlp file tells the game to do different things depending on what parameters you give to it.
In this case a software web site just linked to the file without any parameters, which would cause anybody that clicked the link to see the game editor and not have any idea what to do or what they could make with it.