Apparently IE9 opens a background connection before sending the main HTTP request, blocking a single process server like HTTP::Server::PSGI. See also #191 for a similar issue with google Chrome Incognito mode.
Would making HTTP::Server::PSGI asynchronous be an acceptable solution?
No, that would complicate things and probably require external dependencies. If you need asynchronous web server that supports PSGI we already have plenty of options.