Well, you're using the available() method, which is almost always a bad idea in the first place. And you're using it badly, too. If your LoggingThread tries to read before the ServerThread has written anything, then the while loop you have there says "Anything available? No? Then we're done." Any data which comes in later doesn't get read.
Which is your problem description, right?
So get rid of available(). Just read from the input stream until you reach the end of the stream.
By the way, here's the Ranch's FAQ entry about that:
Available Doesnt Do What You Think It Does.