When I browse sites over HTTPS (specifically GitHub and Twitter) it sometimes works, but mostly it doesn't. Web pages often fail to load and my web browser shows that "the server unexpectedly dropped the connection". The fact that I sometimes (after a few refreshes) can browse over HTTPS means that my ISP isn't blocking it completely.
I'm with a small ISP which re-distributes their combined ADSL & cable connection wirelessly throughout this city. I connect to them via a wireless antenna on the roof, and a router in client mode uses this antenna to provide the Internet connection to other computers in the house via Ethernet.
This ISP is by no means a good one, but my experience with browsing over HTTP is significantly better than over secure connection. I would like to figure out is it their fault, their own ISP's fault, or is my router busted (it seems to work fine but its web interface often hangs for a few minutes, indicating that the device is not perfect).
Note: I have very low upload speed (0.4 Mb/s) because all ISPs in this country provide at most 1/16 (or, rarely, 1/8) upload/download ratio. My ping to my ISP's router isn't great, either; it varies wildly between 3-400 ms.
I need suggestions for tools that I can use to analyze my network traffic, inspect HTTPS connections and possibly see where or when they fail. I'm on a Mac running OS X.
Update: it seems not a problem with the ISP, but with my browser (Safari). I just tried other browsers and they all load GitHub fine, while Safari is still the only one that can't. Another Safari on the other laptop also works fine. I will try to remove browser plugins to see if it has any effect.