Talk to him, one on one. Why wont he sign? Does he still love you? If the case is so, explain to him that a one sided love wont work out.
Ask him what hes afraid of, the fact that he wont ever find someone else? assure him he will and that he has lots of people to love him.
Ask him if hes worried about the kids, if so, reassure him the kids are both of yours and that you will work something out, or leave it to the kids.
When asking all of this, keep a calm and collected attitude and DO NOT be icy or cold or shout AT ALL, you have to reassure him as much as possible to lull him into signing it.