Every common database has some tools to backup your data.
e.g.: PostgreSQL --> pg_dump, MySQL --> mysqldump
Look at the documentation of the backup tool from your database and use it for the entire schema/database of you application.
This approach is more general and much more reliable than application built-in backup functions/plugins.
If you application depends on files on your filesystem too, than you have to save them too (recommendation: rsync)
It happens because your allowed memory size is exhausted, and the DB is quite big, and it takes more time.
An Allowed Memory Size Exhausted error means that your WordPress installation doesn't have enough memory to achieve what you want. You can try out the following steps:
Increase your memory limit in wp-config.php
Increase your memory limit by editing php.ini. This is not a file that comes with WordPress so if you are unfamiliar with it you should contact your web host about increasing your memory limit.