If your doctor says no then see someone else because yes it can be saved by someone who knows what they are doing.
Please don't let the surgeon tell you otherwise because if he does you don't want him operating on you.
Providing your ovary is in good condition yes. I had a 7cm simple cyst removed april 2010. By Nov new one came back, mine were in ovary not on it. Feb 2011 he started with a laparoscopy that turnes into a laparotomy and had to remove my ovary, because it was weak and the cyst though it was smaller than the first one, it collapsed my ovarian wall. Even if you do wind up having to lose the ovary, it'll be ok.
Saw my dr. today for a 6mm possible endometrioma cyst and he described the surgery to me. He will use three openings in the abdomen (small) and a fourth cut so that they can see the ovary and insert a type of bag that will capture the cyst and keep it isolated from the body cavity so nothing leaks. He will then line the ovary where he removes the cyst and sew it up. The entire thing will be no more than two and a half hours. I go home the same day. Yes a good dr. can save the ovary.