It's likely one or more of your Perl modules that the VI Perl SDK depends on where updated. There have been some ongoing problems with the VI Perl SDK, Crypt::SSLeay, and LWP.
The VI Perl SDK uses Crypt::SSLeay (to get non-verify certificate handling in the SSL handshake), so they force it in. But that lib is only maintained for backwards compatability, and LWP prefers IO::Socket::SSL (which requires you have some certificate handling against MiTM attacks, though you can pass SSL_VERIFY_NONE if you use the some client defaults in the library vs LWPs pass through ssl_opts).
I've also had problems with LWP 6.08? + VI Perl SDK. Some have had luck with LWP 6.03 (downgrade), others have had success with GAAS/libwww-perl-5.837.tar.gz. I built a raw, low level Perl lib around the SDK using LWP 6.08 + IO::Socket::SSL, no issues. So I suspect some of the protocol issues and extremely slow connection initialization issues being seen are from Crypt::SSLeay + newer LWP versions. Problem is the VI Perl SDK VICommon.pm basically forces the use of Crypt::SSLeay.
What's your version of LWP (libwww) installed?
perl -MLWP -e 'print "$LWP::VERSION\n"';