Engine cuts out when trying to accelerate

have you changed the fuel filter? or maybe try a fuel system cleaner and see how it act.

O2 sensor or wiring, if its not a consistent power loss/idling issue: pre-cat 02 sensor, the one in the front of the engine it is the important one, you need a special tool, its not too expensive to have a mechanic do it. I.E your fuel to air mixture is getting screwed up, for some reason 35-45, and 50 -65 mph tend to be where you notic, otherwise its your transmission going out.