There are 2 ways to apply the Arc warp to an object:
Effect > Warp > Arc
Object > Envelope Distort > Make with Warp > Arc
If you use #1 above, then the effect is created relative to the artboard. This means is you rotate or distort the object with the effect applied, the effect remains relative to the artboard edges and will not rotate with the object. As Bakabaka answered, if you use
Object > Expand Appearance after applying the effect, you "bake in" the effect making it no longer editable and it will then rotate with the object.
If you wish to retain the live aspect of the warp so it can be edited again later if needed, AND have it relative to the object use #2 above. This applies the distortion (warp) relative to the object, not the artboard. This way the envelope is still editable regardless of how you may transform the object. There's no need to expand the appearance if you use the Envelope Distort rather than the effect.
I rarely use the Effect due to this very vast difference in the relationship of the distortion to the object.