If the connection is tied to a MonoBehaviour you can just call DontDestroyOnLoad on that object.
Something like this
DontDestroyOnLoad( connectionObject );
You can read more about it here.
Note: you need to destroy the object by hand by calling Destroy when don't need it any more.
If the connection is not tied to a MonoBehaviour you need to keep a reference to it from an object that is not destroyed, for instance a Singleton.