Wow! You hit the nail, oba!
Indeed it's related to Avast Antivirus! I also it have installed. I'm using Avast for years but never had such problem with Gargoyle. For test I disabled Avast, and the Gargoyle webgui issue does not appear, indeed!
Actually there was an Avast program upgrade (to 2014.9.0.2011 program version) recently, and probably that started this problem, which I didn't recognise. In previous Avast version (2014.9.0.something) there was no such issue.
So I wonder whether the Avast latest or the Gargoyle is the wrong, but it's rather Avast problem, not Gargoyle.
In Avast I added a while URL to here, but it doesn't work (I'm using Hungarian interface of Avast so the English strings might be not exact):
Avast Settings > Active Protections > Web shield > Web Shield settings (small wheel at right side) > Exceptions > White URL:http://192.168.0.1/*
But this doesn't solve the problem yet.
Thanks a lot for this Avast info!