Stable, yes, until it's not. The OP point was that in case of an extraordinary event of a big enough scale - which your definition of a stable society doesn't exclude - most(?) of the people won't make it because of the very different nature of these relationships. So, while a disturbance is less likely, its effects would be more dramatic.
I don't think this is accurate. We are much less likely to suffer famine than they were (also epidemics, despite recent events). We are much less likely to suffer war. We are much less likely to suffer a neighboring warlord taking our stuff, including the food we need for the winter. And so on.
Viewed from a high enough level, the society may have been stable. Stability wasn't really a characteristic of life at the individual or family level, though.