So I spent hours today trying to figure out a problem with my install of the 747v3. I nailed it down to my PFC 737 Desktop Yoke.

The 747v3 doesn't like my Yoke. When ever I set up the Elevator and Ailerons axis in FSUIPC using the PFC Yoke the Auto pilot continuously disconnects. If I change the Elevator and Ailerons mapping to my X55 Stick no problems. As soon as I change the mappings back to the PFC Yoke the problem returns. Ive calibrated the Yoke in Win10 and in FSUIPC. This problem only happens in the 747v3.  I have no problems with the 777 or 737NGX.

Any tips?

I bet you have something else assigned to the yoke.  I'd forget setting it up in FSUIPC and instead set it up in FSX or P3D (whichever you have) as a test.  Also increase the null zones on your yoke.  I was setting my autopilot and hung my headset on the yoke and AP disconnected every time (I never notice the yoke moved ever so slightly) but it was enough to shut off the AP.

The null zone fixed it.  If the yoke is not perfectly centered the AP will disconnect. As the PFC Yoke doesn't have springs you can't feel the center spot. It does self center when I release but it's only got to be at a tiny bit off and the autopilot will not connect