Without seeing your results, it is hard to tell, but my inclination would be to say that you could be getting incomplete fusion with the copper. Copper is a much much better conductor of heat than stainless steel, so it will take more energy to get it to melt. My first suggestion would be to preheat the copper in order to keep it from conducting so much heat away from the fusion zone. Additonal details would be helpfull if this does not solve your problem, such as what thicknesses are you trying to weld, and what process are you using. GMAW, SMAW, etc.? Are you currently doing any preheating. What kind of joint are you using?