I was unable to get the Broken Link Checker plugin to find https links. It kept giving me an unknown error. I finally found the solution to the problem. My PHP5 install did not have the CURL Extention installed. I used the Digital Ocean LAMP image to setup my server.
This is the command that fixed it.
sudo apt-get install php5-curl
Then I rebooted my server and had broken link checker check all my links again. The problem was resolved.