Ok, this tells me some things.
First of all: sorry for the delay, holidays and such.
Second, Fiddler is a great little program for catching 'lint' in web apps to debug issues. If the action of running Fiddler is fixing your issue then this is positively a client side issue. My best guess is that there is an issue with your proxy server and how http or https requests are being handled either by the server or by your machine/code.
I would take a look at the fiddler log with your IT to determine the proxy requests. Remember that when running Fiddler it is involved with the requests and not just monitoring traffic. This act of Fiddler as a proxy is (my best guess) why the http or https requests are going through while Fiddler is operating. Since this same issue occurs on both networks I would further my guess that this is a personal machine firewall causing the proxy issue.