I think you have a basic misunderstanding as to how a staging site on WPEngine works. To make a staging site, WPEngine clones your live site. This is good because it allows you to test code without impacting your live server.

We developing enterprise-class software, we always use 3 or more environments. At the most basic level we use development, staging, and production environments. Development is an isolated environment where the actual code writing takes place. Staging is a clone of production where we test code integration before moving to production. If everything works in staging, we move to production and perform another round of regression testing before releasing to the public.

When WPEngine publishes a staging environment to production, it clones your staging environment to production. Cloning completely overwrites what was there before because the database is cloned, not just WordPress.

When I've worked in WPEngine staging environments and came to the point where I had to publish to production, there was a way to select the tables you want to copy back to production. Don't copy the tables that contain entry data, frm_items and frm_item_metas. If you're creating custom post types, don't include wp_posts or wp_postmeta. None of your entry data will be overwritten.