I don't have statistics on poly relationships, and I doubt that anyone has good statistics.
Still, so far as raising children is concerned, I think you're conflating two situations. A poly relationship might be considered unstable if one or more people leaves, but if a core group remains raising children, it might be more stable for children than a couple that breaks up.
A thought occurred to me today as I skimmed an article in a rationality forum where the subject of gay marriage cropped up; seeing as the issue has been hotly contested in various public fora and especially the courts, what about poly? After all, many if not all the arguments for gay marriage apply to poly marriage as well.
Questions for LWers who are currently in a such a relationship, or have an opinion to share:
Do polies want to marry each other or do such relationships not lend themselves to permanence above a threshold of partners? Should polies campaign for the right for a civil union anyway? what are the up and down sides of this? etc