You can’t have apnoea for four minutes — you'd then be brain dead.
Hypoxia is lack of oxygen, but isn’t necessarily life-threatening.
A brain injury wouldn’t necessarily affect your airways, either.
It’s irrelevant, anyway, as Madeleine didn’t fall and fracture her skull — she was abducted.
You have yet to show us any evidence that she was abducted.
Do some more research. I've worked in critical care for 30 years. If someone is unconscious they can lose control of their airway (particularly so in children because of their anatomical differences with adults), the tongue could cause an obstruction of the upper airway or the regurgitation of semi digested food could cause airway obstruction (why do you think people are nil by mouth before an anaesthetic?). If a person's airway is totally obstructed (not uncommon after head injury) the resultant lack of oxygen to vital organs (hypoxia) would be critical after four or five minutes. The lack of oxygen to the heart would cause cardiac arrest after about four of five minutes of apnoea. Children become hypoxic much faster than adults. It's fantasy to pretend that death after unconsciousness caused by a head injury isn't a possibility after four to five minutes.
The sedative properties of phenergan are not a rare side effect. They are
expected in a normal dose. I've met medics who openly use phenergan for travel sickness in children knowing they are going to have a very peaceful journey.