I have a 2006 F150 with 5.4, and after truck warms up and you try to accelerate it stumbles as a misfire and also if I release the gas peddle it also does the same thing, I changed the plugs and coil packs but still have same symptoms, had truck checked code for misfire but there were none, mechanic thinks it could be the timing solenoids, this has been going on for a while, is this possible

 

Throw some Techron in the gas, you may have dirty injectors.

 

It's worth a try

 

It might also be the VCT.

 

I was thinking that also but nowhere gives conclusive symptoms