Yes well... that might to do with timeout errors on the php settings of the server. If normal backup via phpmyadmin does not work and via mysqldumper would work, then it's a server side issue mostly.
Best way to make a database backup would be via SSH then if you have SSH access.
Again, for both setting timeouts higher or to allow SSH, you have to contact your own hosting provider.
There are some mysqldumper alternatives but I don't know which is good to use.