Did you fix it cause it seems to be working...
to test I selected lost password.
entered test@test.com
entered the captcha
Clicked on the button
And it came up with the response "The email 'test@test.com' does not exist on this site."
So it is working so far as it's interrogating the database and seeing the email doesn't exist.
Just had another look, and the only logic I can suggest is there is a slightly different server setup. As clicking submit takes you back to the home page.
I would go so far as to check that timeouts aren't going to be an issue at all.