This behaviour is undocumented.
The most excellent Claes Jacobssen told me how to fix it on IRC, but the fix involves using an undocumented package supplied with SOAP::Lite in an undocumented way. From what I can tell, the philosophy behind the documentation for this appalling module is "it was hard to write, so it should be hard to use". This is, even though it appears to work, AWFUL software.
Of course, it doesn't help that I'm having to expose my SOAP::Lite-ish server to another piece of awful software -