I would think that sleeping for a second or two on the redirect might help. Also check for values that your browser may be POST'ing when the redirect is thrown. These are the two things that have screwed me up in the past with WWW::Mechanize.
I had problems with redirected posts as well. See
LWP::UserAgent Docs. LWP::UserAgent does not follow redirects for posts by default, you have to tell it you want to do that.
Since WWW::Mechanize is a subclass of LWP::UserAgent, you should be able to: