How long can a concrete pool stay without the water?
Depends on where the natural water table is and how much pressure it can put on the pool (which is a function of the porosity of the earth immediately surrounding the pool).  If you know the bottom is above the water table you can leave it empty until the ground freezes.  Otherwise you're counting on the water table level and surrounding soil to not exceed the pressure from when it was first built or last empty without damage.

There is a countermeasure built into most pools: they have plugs you can unscrew or pop open when drained that provide a conduit for water to drain in and out of the ground.  But again, those are only as good as the sub-surface porosity at relieving water pressure on the pool shell.