I think what you mean is that the relaxed protein will still fit the density, but seems to wander off from the original coordinate frame.
Assuming you are NOT using coordinate constraints, this is normal. Rosetta uses internal coordinates; small torsion changes near the root of the internal folding tree (probably the N terminus) will have large lever arm effects on oritentation relative to the origin, but no effect on physics. Realigning to the input model will repair this, since you have density fixed to the origin.
There are modes for relaxing proteins with the density present and active in the scorefunction you might wish to use instead. (I am not an expert there).
.
