"To preserve the relationship" means to maintain and protect a positive connection or bond between two individuals or groups, often by avoiding conflict or finding ways to resolve issues peacefully. Full definition
It can also help preserve your relationship with your teen, as even very skilled and safety - conscious parents might not have the time or temperament to be the best teacher. (kanor.net)
When parents live in separate homes, a special challenge is presented in preserving the relationship between children and both parents after divorce or separation. (familylawmatters-blog.com)
Both partners in a relationship need to make positive changes for the sake of preserving the relationship (e.g., item 4). (scirp.org)