It's an 09 FXDC, Dan. It has a 96" injected motor.
You may want to check your plugs and plug wires, if you haven't already. I don't know how old that gas is in the tank but it may cause some issues. Try draining the tank, put a few ounces of Seafoam in there, and see what happens. That's not a whole lot of miles on an 09.
I had an 07 FXDC and loved it. Swapped it in for an 07 Ultra Classic because the wife hated the seat and we really couldn't ride very far comfortably. If Mama ain't happy, ain't nobody happy. When I first test rode the Ultra, I IMMEDIATELY noticed the difference in performance/acceleration due to the weight difference. (I mentioned to the salesman that it was a dog in comparison.)
Good luck. Hopefully it's nothing serious. Sounds like it's switching to a lean map when the motor warms up and goes into open loop. Check your codes.