The salutations found in the closing verses of several New Testament epistles should inform some of our understanding of inter-church fellowship. I cannot help but be impressed with the Christians' knowledge of one another across the Roman empire (without planes, trains, automobiles or telephones, television, and the internet) -- and beyond that, the affection they had for one another and the esteem in which they held one another. Contrast that with the apparent complacency and indifference in our modern churches, often found within no more distance than one county, when people in "sister" churches across town don't know one another -- sometimes even within a local church if it is a large one.
Romans chapter 16 is filled with greetings. We cannot help being amazed by Paul's acquaintance with all these people. But we might fail to grasp that the persons mentioned must have also been well acquainted with one another. These different ones that Paul, Peter and others saluted and wanted to salute others apparently made connections in person, for they were to greet one another with a holy kiss. Phebe was a servant of the church at Cenchrea, yet she probably missed a lot of her own church's services while carrying a letter to the saints at Rome (Romans 16:1). Certainly she was engaged in the work of the Lord, but she also was "away from her post" at her home church. To me these examples and the practice of the New Testament church do not fit well into the "you must always attend your own church services" model that some strenuously advocate. Surely this is the norm -- service to the Lord through our local assembly. But if we draw up within ourselves -- and many of us have -- we won't look like the New Testament churches and we won't know anyone to greet!