I had a similar issue with a crank sensor. It was replaced and worked well for about 6 months. Then every once in a while it(motor) would cut out just for a split second. It progressively got worse until it would cut out about 6-10 times per half hour of running.roughly 10-15 after starting that it dies
At it's worse it wouldn't cut out until 10 minuets after starting. Just enough time to heat things up. I replaced it with a delphi part from rockauto and truck is running fine now. Where did you get the sensor? Pep Boys? Crank sensors are hall effect sensors usually 3 wires positive voltage negative and then the signal. If you have a wiring diagram of your truck and can find the signal wire from the sensor going back to the pcm you MAY be able to see if it's getting a signal. Do you have you old sensor? Since you are still getting the code 11 it has to be in the crank or cam sensors or the wiring to or from them.