Boffin, my family history appears to apply to first babies only. I don't know what it is that causes it, but of the 3 generations I know of:
I (first baby) was born after 3 days of my mum being 2cm dilated (at 40+8) & lots of prodding & induction. I was almost a CS baby, especially after her waters were broken & found to be meconium stained, with my heartrate taking 30+ seconds to return to normal after each contraction.
My mum (first baby) & grandma both nearly died during my grandma's labour (my granddad was actually asked who he wanted them to save) with a very similar thing, including an emergency ambulance transfer from the hospital to a bigger, specialist hospital, ending in an emergency CS.
My great-grandma lost her first baby (my grandma's brother) after what seems to have been almost identical circumstances again - although this is obviously quite a while ago (late 20s, I think) & not really talked about given the outcome.
I'm not sure about before that, but it doesn't look good. At least next time should be easier