I cannot download new firmware for an Apple device
First, please make sure that the internet connection is working. The network connection can be verified in login screen > Settings > Set Network Test > Ping www.example.com. The network connection can also be verified in the BMDE main view in the bottom left corner - the pop-up from the network symbol should show 'Network is OK'.
Then, please make sure that you are able to connect to Apple servers. Make sure that the firewall is not blocking the Apple servers (see firewall settings and hardware requirements from the BMDE user manual available from the BMP - “Help” and then “Products” page). The network connection to Apple servers can be verified in login screen > Settings > Set Network Test > Ping itunes.apple.com. A better way to verify the connection to Apple servers is to test the same network connection with a normal Windows/Linux PC: try to open 'http://itunes.apple.com/check/version' in the web browser - it should return XML file from Apple.
Also, please check that you have enough free space on your hard drive, instructions on how to do this can be found in the “Storage Cleanup” section of the user manual, or if you are not using a permanent installation for BMDE, make sure you have enough RAM for storing the firmware images.