You shouldn't close your connection. You will use the same connection for future queries this process of closing and opening it again will just consume time and resources. Better if you have a persistent connection and close it only when your program ends.
It's like working on a restaurant and everytime you end to cook something you throw your utils and go to a store to buy them again.
It would be to have a connection pool which is just a group of connections that are already connected and could be used to serve more queries. This is pretty normal and it's a pattern that many frameworks and libraries implement under the hood.
I recommend you to read more about a pattern named object pooling and moongose official docs to create a connection pool.