If you are the LD or ND person married to an HD spouse, what is your motivation for preserving the marriage when it's been SSM for a long time and the lack of sex has not bothered you? If your HD partner suggests divorce, but also makes it clear that he/she wants to remain a good friend and a cooperative parent to your kids, what are you afraid of, or what is it you want to keep? Is it the possibility of a future sexual relationship? Is it just the companionship of living together? Is it the public embarrassment of being "dumped" and having everyone wonder why you "couldn't keep your spouse interested"? Is it the jealousy of giving your partner up to someone else? Or is it just a general fear and uncertainty about the influence a new partner of your ex will have over your ex and your kids?
If you're bothered by the image of your ex having passionate sex with a new person, why would you feel that way if you didn't want to have sex with your partner in the first place? As one poster here mentioned, if sex didn't matter to you, why would it matter to you that your ex was having it with someone else?
Or is the premise wrong? Does the lack of sex bother you in the sense that you know you SHOULD want sex, but you know you don't?
It's probably a combination of these things, and other things I can't think of. A mix of your own fears and insecurities, and not just because of your love for your partner? If you truly only loved your partner in an altruistic way, it seems you might even be happy to have them find someone who appreciates them sexually, no?