Should our sofa tournament replay a round after a controller disconnect?

My controller disconnected while I was ahead with twelve seconds left. I stopped moving; my cousin scored twice and won. He offered a rematch immediately, but another player said, "You can't rewrite the bracket because your battery died."

This was an eight-person tournament in my living room, with a homemade cardboard trophy. I'd written down the match order, but nothing about equipment failures. I was also the organizer, so whatever I decide about my own loss will become the rule for everyone after me.

My cousin thinks keeping the win would look cheap. The player waiting for him thinks a replay could delay the whole evening and wants the bracket left alone. I don't know whether the battery ran out or the controller briefly lost connection; nobody checked before the argument started.

What is the fairest way to handle this one unresolved round, and then set a rule that I would accept if I were the person who had just benefited from the disconnect?