if the mount tabs are broken, yes it will move, as the airbox itself is also the bracket for the throttle body.

if you have a pick n pull nearby, IIRC they charge about $20 for the airbox.
( i bought a backup in case i ever pull my CAI. when Previous owner installed the CAI, it didn't come with a bracket for the throttle body, so he just modified the airbox to where the Tube would just pass through.)

 

Have you tried a fuel systen cleaning product before noticing this? Only reason I ask is I ran a bottle through my dakota along with shell v power which I try to do once a year. The last time I did it I noticed a large mpg drop from 18mpg to getting 80 miles from half of a 22gal tank. I disconected the battery over night to let the pcm reset and when everything reset it was back up.