What type of site are you trying to back up here (CMS, forum software, web builder built side, normally coded site..)?
You should be able to manually grab the backups. As
@Dead-i said, cPanel's backup feature can get a bit heavy. This could be due to the fact that it has to try setting up the structure of the zip (by that I mean the directories and where the files go) and placing the content into the zip, possibly more could be involved in the process (I have never used this feature before so this is just a guess).
You should be able to place the manual backups on your desired host (without cPanel restore), more work but at the end it'll be there.
If your site uses the database then you'll need to redo the database users in order to connect.