I have a file in AutoCad with ETRS89 coordinates, and when I use the same map in ArcGIS it loses coordinates. With other files do not happen.
Which version of ArcGIS and Autocad are you using?
This is esri's help page for 10.1
but you need to make sure ArcMap is a newer version then the Autocad Version you are using or save the dwg file as either 2004 or 2007 version file. ie you can't open Autocad 2011 files in ArcMap 9.2. The other idea to try is to go to the dwg file through ArcCatalog and assign coordinates to the file using ArcCatalog before importing it Autocad.