There is "pronounce death", which is a legal action, and "cease care" which is a medical one. We tend to mix them mentally.
Usually the person to declare death has some sort of legal standing such as a medical examiner, doctor, law enforcement officer (sometimes THAT doesn't work out too well). A TECHNICIAN (and everyone except MD's and nurses on the scene are technicians) generally cannot DECLARE death.
Cessation of treatment in the field can be due to exhaustion, obvious death (rotting, decapitated, or similar), lack of vitally necessary supplies, impending danger to rescuer, relief by competent caregivers, delivery to a receiving facility.
Particular states may have their own protocols. (As always...<_< ).
Pragmatically, even just considering CPR: perfect CPR is no more than 30% effective and dwindles fast as you tire; without defibrillation (even AED) every minute is supposed to mean a 10% loss of the likelihood for recovery. Without resuscitation or respiration clinical, death ensues in 3 min, biological death at 5, absolute biological death at 10.