Syncope does indeed, nowadays, mean a faint. But I think that in the past it was used more to cover any loss of consciousness but especially due to shock (as in physiological shock, eg blood loss, not psychological shock eg fear or surprise!!)
So this poor lady had a prolonged labour before the baby was actually due, and may well have lost too much blood during this, causing hypovolaemic shock = syncope.
(but if so, nowadays the order of these two would be reversed on the death certificate. The cause of death would be the shock, which in turn was caused by the labour).