OK you tried to put logfile.open() in displayGPS, and that created many files, all with one line in them.
You want just ONE file with multiple lines.
well it seems that because the logfile.close() is being done when the code HAS AVAILABLE data, it only writes one line then closes the file and does NOT reopen it. You need to take that .close line out and put it somewhere when there is NO available data. That way it will still write the data to the SD card and only close when there is no data. You may need to tell it to close with a button when you go to shut down the ARD.
I'm not sure if Arduino has a way to update the file when it is created instead of constantly creating new files each time. Look into that.