If you pass an https URL, then PostString will just handle it all by magic. If you're getting a timeout, then you most likely have a network problem. Do you have any other tools you can use on the same network to check the connection to the URL you're trying to reach. For example, if you have OpenSSL installed (on Linux, Mac for instance). you could use the command
openssl s_client -connect example.com:443
to check that you can make a connection from your network to that address, on the default port used for SSL. Then entering
will retrieve the server's home page.
Can you browse to the SSL port on that server? (Not much good if it only accepts POST, but there should at least be some sort of page).