M36 is the fuse for the right hand outlet; the one that is always hot.
It gets power directly from the battery bus, so there is no computer involved.
That leaves only a few possibilities.
Bad fuse. Did you try a new one, even though you believe it to be good?
Bad connection at the back of the socket. I have seen several posts where that was the problem.
Bad connection at a splice somewhere along the wire.
Broken wire, hidden by the insulation.
2008 Unlimited Rubicon Automatic