Resume download on DB exporting
If you have remote access to the server you are transfering I suggest you make a full back up of the database put it in a FTP or torrent (last option not very safe but easier if you don't know how to build a FTP server). Then when the file is transfered to the other server, you restore the backup.
This option will save you the trouble with the internet since the transfer to files will be local and FTP or torrent transfers can be paused/resumed if case of connection failed.