Brain "death", cardiac "death" and all forms of clinical "death" are all forms of legal fiction. A person is dead when they are a decomposing corpse and alive when breathing, heart beating and thinking - the exact point of death is often indeterminate but the two opposites are clear. You cannot bring the dead back to life, but people whose hearts have stopped have been helped back to full function of life and "brain dead" people too have recovered given adequate time and support. The reason (most) organs cease to be viable for transparent in time is because they start decomposing quickly after death. If you keep a person alive as you carefully cut their organs out you can quickly transplant them with minimal damage to the individual organs and high rates of transplant success. If transporting the organs is done without care (especially cooling) and most importantly speed the chance of successful transplant is low.