I've run into this problem when I try to play as well. This is all speculation, but I think it's because of the server rotations that were programmed in. Back when everyone was playing Demon's Souls and the servers were populated this was no big deal, and helped prevent you from being grouped up with the same people over and over. But since it seems you're only connected to people just as you start playing, then I've come to theorize that you start in the most populated server, and actually get rotated into an unpopulated server. When you aren't connected to anybody else, then the game won't allow you to leave messages and acts like you're basically offline.
Long story short; whether this is the actual issue or not, it seems you are only connected to people for the first few minutes of playing. After that for some reason it becomes a ghost town. Just restart the game and you'll have a few more minutes of connectivity.