Technically importing demo contents are multiple processes which download media files from demo server to your server.
So we are using the most completed importer script available in the market. However if there is some limited setting on your server which kill importing processes when it reaches certain level of server resources usage. It’s related to your server limitation.
Normally we can try to find other workaround for you to see if it works by using other plugin to manually import content first then try to import all media files later. To see if it’s working.
But these workaround required your WordPress login information so we can try to do it for you. Please submit your question on Please also add a link to your site as well as the login credentials when opening the ticket, so we can install theme and demo content for you.