If the Gallery is hosted on a different physical computer to the rest of the site, the problem might be there but I don't think it is. Other than that, it sounds like it might be due to a misbehaving transparent proxy. You could try setting an explicit proxy server in your Internet Connection settings and see if that works (your ISP probably has one or more you can use, or you can try a public one but they tend to be very slow). Make sure you do not have the "Auto-detect proxy" or similar option ticked unless you are sure you need it.
Another possible culprit is a firewall (hardware or software) blocking the port the server wants to use to transfer the file. Also, some higher-end firewalls will detect the type of file transfer as a .JPG and block it as a part of company policy.
Good luck, Bob.