I think this is unrelated to the version of Windows. I tested the latest (2.5) release of Remote on Windows XP Home 32-bit, Windows 7 Home Premium 32-bit and Windows 7 Home Premium 64-bit. All worked like a charm. I think that you have a problem with your Internet connection, or your firewall.
First, make sure that you are using the latest release. It's Akeeba Remote Control 2.5, launched just yesterday. Find it in our Download page.
Then, retry backup. If it fails, right-click the name of the site, click "View Log", in the new window click "Save as a text file". Then put this file in a ZIP and attach it to your next post in this forum. This will help me understand what is going on.
Nicholas K. Dionysopoulos
Lead Developer and Director