Looks like you should bug the maintainer of LWP :)

https://rt.cpan.org/Public/Dist/Display.html?Name=libwww-perl
Bug #75908 for libwww-perl: digest authentication's stale nonce not handled
Bug #70789 for libwww-perl: LWP::UserAgent: HTTP-Digest authentication fails if server uses realm with comma-char (',')
Bug #43354 for libwww-perl: Error in Authentication Digest Implementation()
Bug #24711 for libwww-perl: LWP should recalculate digest auth after redirects
Bug #20889 for libwww-perl: Error in Authentication Digest Implementation

In reply to Re^4: LWP not working with digest authentication by Anonymous Monk
in thread LWP not working with digest authentication by sophate

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