Dimensions are not directly related to a drawing, but thru a drawing to a model (assembly or part), and when replacing the model parent in a drawing, dimension lost their references (dimension does not know what is being measure in new model attached to the drawing). One way to maintain the mos of the dimension when changing models in a drawing, is by using same base model, modified and keeping as most as posible all sketches and features.
Hope this helps to answer your question :-)
I'd look at the way you are creating your new files, and change it so you don't have this problem. I believe if you start with the drawing and part file open, then do a save as from the part file first, you should be good. After doing the save as from the part file, close both the drawing and part file, then rename your drawing file via windows explorer.
Pack and go may do the same for you also, but I'm a bit pre-pack and go with the above method.
It has been my experience that deleting and recreating the dimensions and centermarks is at least as fast as reattaching them and it is much simpler to accomplish. Notes are usually faster to drag to their attachment than to recreate.