Because energy is released when the phosphate
is popped off the ATP, it takes
energy to reattach
a phosphate back to ADP
(to reload the spring).
The energy to re-assemble an ATP molecule comes
from cellular respiration. Essentially,
this comes from burning sugars in the presence
of oxygen inside cells (in mitochondria, actually).
Note that cells reuse the same ADP/ATP core many times
over -- otherwise we would have to have an enormous
caloric intake every day just to stay alive.
The respiration process is around 40% efficient --
60% of the energy is lost to heat.
By comparison, cars are around 25% efficient in converting fuel to energy.