I tried your script and it works here. So your problem may resides in some module you used. Here I am using:

• Perl 5.6.0
• OpenSSL 0.9.6
• Net_SSLeay.pm v1.18 Crypt-SSLeay v0.37
• Net::HTTPS v 1.2
• LWP::UserAgent v 2.1

Probably I'm not using the newest modules, but I hope these information can help you figure out what happened.

Ciao, Valerio

update: changed used modules