I am a permanent resident and US Green Card holder and looking to travel back to my native Ukraine for 1 month. When I entered US couple of years ago, my Ukrainian passport was stamped with a refuge visa. Would there be a problem for me to return to US? Am I going to loose my green card? My refuge status changed to permanent resident.

It will depend on the facts of your case because of the basis for your permanent residence, you should consult with an experienced immigration attorney.