After updating the HUB to the latest version 4.5.2126.1, I have updated iClone 7, and when it finished, it now keeps claiming I am not connected to the internet, and therefore cannot update anything anymore. I have tried rebooting, but the HUB simply doesn't work anymore. I can make manual updates from the product's help menus, but not from the HUB. I can use the HUB's "products" tab to download products, but the "Updates" tab is now blank, always claiming I "not connected to the internet".

I have attached a screenshot of the error message. 

Mine does the same. But I believe it is not the hub problem. RL servers are extremely overloaded by CC3 release "stampede" and cannot respond in time to hub inquiry.
And same goes to member page. It loads and then it does not on next refresh.

Indeed, I came to the same conclusion after doing some tests. For example, I have tried a ping to "reallusion.com", and was getting 100% packet losses. I wasn't able to login into my account, or even to this forum. I have tried again after dinner, and I was able to come here, but still not able to use the hub or get into my account. 

The servers are stressed out.

whould you try logout and login again?

As stated above, the issue was only happening during the initial download stampede on the CC3 release date. Things appear to be normal now. What apparently happened was that the HUB was unable to connect the RL servers due to the unusually high traffic. The problem was that it jumped to the wrong idea that I wasn't connected, when what was really happening was that the servers were too crowded to reply. In a way, that needs to be fixed in the HUB so it can correctly identify what is what when it fails to connect. It was indeed unable to connect to the RL servers, but it's giving us the wrong error message.