My guess is that there is a problem writing on the device. Does CC say anything when it disconnects? Make sure that the fire is not out of "disk" space.
If you send me a CC debug log (
instructions are here, please erase the multipie.co.uk address) I might be able to say more about what is going on.
Are you sure that the mac and pc are running the same version of calibre? I would expect the line numbers in the error message to be the same.