Is there a way I can setup my connection in such a way that a row doesn't get removed in the destination table even if the corresponding row in the source table has been removed? Our source tables are cleaned on regular basis which makes it hard to have persistent data.

Use full refresh append or incremental append method

What if I have to add tables to the source configuration? Airbyte gives warning about having to delete the destination tables when the configuration is changed. Here's an example:

In that situation you need to create a new connection, at the moment is a limitation adding new tables without deleting/re-creating the catalog

what if backup the table and then copy it back into the dataset after updating the schema? Will it break the synchronisation?

It's an option but not easy to maintain