People often underestimate how gruelling and how relentless it is to raise children. Add in children with disabilities or additional needs and it becomes a whole new ball-game.
Probably there are times that both parents would like to walk out but society only really accords that option to men. Women are expected to stay and to cope, and the weight of that expectation is a heavy one. Because failing to cope is not only going against societal expectations but also letting your child down. If you (not your male partner) are the one they depend entirely on, then you feel that you are letting them down if you leave in a way that an often already disconnected father is not.
I'm not sure forcing men to stay is necessarily the best option. An already-shit father who didn't want to be there would struggle to deal with the frustration, the lack of recognition and the thanklessness that comes from raising high-needs children, day in, day out, and might become stressed, abusive and possibly violent. Yes, they shouldn't, it's unacceptable and this is very much a man problem, but probably it's best for women and children not to have inadequate men around and just to be able to focus quietly on their own needs.
Instead what we need is much better financial support and respite care for families of children with disabilities and special needs. The burden of having a child with additional needs should be shared by society as a whole, it should not fall so much upon the parents, particularly the mother. Competent, compassionate, professional help would be so much more valuable to a struggling mother than having a useless ex who doesn't want to be there and does the absolute minimum.
I think the issue of feckless and selfish fathers and how this links in with societal expectations is a different one. Even for men who are living with their children's mother, often they manage to opt out to a greater or lesser extent from the burdens and responsibilities of parenthood. It's a spectrum of disconnection for shit fathers - at one end, the dad who's never organised a playdate for his kids and tries to avoid spending time with them at weekends, at the other end, the father who has fucked off, never sees them and does his best to avoid paying anything for them.