"To maintain the connection" means to make sure that the relationship or bond between two or more people or things remains strong and continues to exist. Full definition
Tools for setting clear and respectful limits while maintaining connections with youth. (sounddiscipline.org)
I give them enough space to let them go safely while maintaining connection. (touchstonez.com)
The connections have already been made: These are professionals who rely on networking for their career and carefully maintain the connections between them. (exclusive-executive-resumes.com)