"SSL handshake failed" when connecting to JBoss via HTTPS

Issue

$ wget  https://site.example.com/ --no-check-certificate --debug
DEBUG output created by Wget 1.10.2 (Red Hat modified) on linux-gnu.

 https://site.example.com/
Connecting to site.example.com:443... connected.
Created socket 3.
Releasing 0x0000000019043230 (new refcount 0).
Deleting unused 0x0000000019043230.
Initiating SSL handshake.
SSL handshake failed.
Closed fd 3
Unable to establish SSL connection.