The All-in-One WP Migration plugin retrieves and stores WordPress data using MySQL/MariaDB (posts, pages, comments, users, and more). A database limit set by the hosting provider may be encountered on severely limited hosting plans.
Here is a list of all the limitations that All-in-One WP Migration has:
The maximum number of queries an account can send per hour.
The maximum number of updates that an account can send out per hour.
The number of connections an account can make to the server per hour.
The number of simultaneous connections allowed.
If you come across such a limit, contact your hosting provider and ask if it is possible to increase it.