A complete stab in the dark but, from LWP::Protocol::https:

"This module used to be bundled with the libwww-perl, but it was unbundled ..."

I recall encountering a problem with LWP::Protocol::https some time ago. The solution was to install LWP::Protocol::https after installing libwww-perl. I've no idea if this helps here, but thought it was worth mentioning.