Just to resume a concrete answer to this question:
If you're having a problem like this look somewhere else, not in your HTTPS setup or PHP GET request and parameters.
I have a problem like this, everything worked on HTTP and when I migrate the system to HTTPS not. I was not receiving the GET variable that I was expecting. After several hours of trying to find some problem related with the HTTPS setup and PHP config and code, the problems turns to be that I was not receiving the GET variable because a JS library, included in the HTML header, was not being included due to new restrictions in FF23 ( https://blog.mozilla.org/tanvi/2013/04/10/mixed-content-blocking-enabled-in-firefox-23/ ). I change the JS include to HTTPS and everything works again.
The solution to this particular question(from Sideshow) turns to be a database problem.
Hope that helps!