Re-joining an Open to LAN SP, new UUID is created for me with empty inventory and default skin

My father and I play together on his single player world using the "Open to LAN" function. Occasionally, when I attempt to join his world it creates a new UUID for me, with a default skin and empty inventory at world spawn. Deleting the new UUID file that does not correspond to a username from /.minecraft/saves/WORLDNAME/playerdata will occasionally fix the problem, but the problem is replicated again at a later date. This has happened to me at least 7 or 8 unique times in the last 2 and a half weeks.