Two things,
one, a better practice when contacting services is to use a known User Agent, such as my $mech = WWW::Mechanize->new( agent => "User-Agent: Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; rv:1.7.8) Gecko/20050511 Firefox/1.0.4"). Many services, especially Google's, tend to disregard requests from unknown agents, or from LWP::UserAgent's default "libwww-perl/5.8"

Two, why not use a dedicated module such as Mail::Webmail::Gmail?