Is the machine you're SSH tunneling into somewhere in your local LAN or outside? If outside, there's a very good chance your local ISP (or router) is dropping your connection to those specific websites (for whatever reason). The reason this works when tunneling is because that SSH machine presumably uses a different ISP/router and is not bound by the same limitations.
If the machine you're tunneling into is within your local LAN, I would check the DNS settings on it and compare it to your local machine. If the DNS settings are different, change your local settings to reflect the SSH machine's settings.