This is a recent behavior of IE 11.x , Chrome 39.x and Firefox 29.x
Maybe this applies to older versions too.
The developers of Internet Browsers decided that they will not let you connect to Sites with self signed certificates.
They will protect you either you like it or not!
They missed that there are millions of routers, switches, monitoring devices that do use such certificates.
Solution 1: Use Maxthon Cloud Browser . You will get some warnings but at least you can continue and connect successfully.
Solution 2: Use Fiddler (The free web debugging proxy) and enable https inspection, before you run the Browser.
Fiddler will produce an intermediate certificate that you must accept.
This certificate is presented to the browser instead of you site's self signed certificate. This way you connect successfully.