Description is enough to go on ... and what "plan' do have with your hosting provider?
Do you have FTP and/or ssh access to your site?
Is apache running as a cgi or fastcgi? Then there is an apache setting that might need to be made
maximum body size of a HTTP request
Was going to suggesting using file system repository for uploading these larger backups so you could take Moodle/Apache/PHP out of the loop with file transfers, but you'd have to have either FTP or ssh access to your site. to do so.
If files transfered to server using either FTP/or scp alternative methods fail then it has something to do with the plan. If files transfered to server are successful, then it's a matter of setting up a category/course for course restores ... setting the only file system repo one needs to be available in that course for restores.
'spirit of sharing', Ken
by Ken Task.