Googlebot can't access robots.txt

GWT has been reporting for several weeks that Googlebot can’t access the robots.txt file on one of my sites. It’s there, and I can reach it via without problem, but using “Fetch as Googlebot” gives me the message “Unreachable robots.txt.”. I’ve made no changes to the site for several months, and no changes to robots.txt for over two years.

Does anyone know what could be causing this and how I can fix it (without deleting the file)?