The process killer is utilized when you’re taxing server cpu, not bandwidth. Transferring files isn’t a heavy load for the servers, so you’re probably not having problems from that.
Is your Windows box formatted with a Fat32 or NTFS filesystem? The filelimit for Fat32 is only 4GB due to the block sizing. NTFS allows 16TB theoretically, but the practical limit is probably something less.
Can you break your archive into smaller parts that are less than 4GB each?