When a saturated solution of Ca(OH)2 is stored, why is it best to be sure that some solid is present?

"Saturated solution of Ca(OH)₂" is the solution which dissolves the maximum amount of Ca(OH)₂ solution at a certain temperature. When some solid of Ca(OH)₂ is present, it means that the solution cannot dissolve more Ca(OH)₂. In other words, the amount of dissolved Ca(OH)₂ is the maximum. Hence, this ensures that the solution is saturated.

So you know the solution is saturated.

Calcium hydroxide reacts with Carbon dioxide, which is in the air. Some will react with the Ca(OH)2 will be used by that reaction.