Oh, I'd love to see a picture of your plant! I love Cyclamen but unfortunately they don't like the heat here in Florida. We find them at our garden centers around the holidays and most folks buy them just for temporary plants while in bloom at that time.
I didn't even realize Cyclamen grew stolons! I thought the only way to propagate them was from seed but you might try to pin the stolons back down to the soil without removing them from the mother plant ... you can use regular old "bobby pins"/"hair pins" for this purpose (found inexpensively at Wal-Mart or any local drug store.) Once the stolons take root and get larger, you could separate them and pot them up singly.
http://davesgarden.com/guides/...
http://www.guide-to-houseplant...
http://www.plantoftheweek.org/...
