Just to add...Hoyt recommends that a modern synthetic (Dyneema, Fast Flight, etc.) string for a high-performance bow have not less than 15-20 twists with a suggested maximum of 1 twist per inch of string length. This promotes a rounder, more consistent string for a recurve.
On keeping the bow strung...bows with modern laminate limbs such as the take down I am asuming..as Pete stated there shouldnt be an issue much like a compound...
Wooden bows however if not being used I would unstring if not being used...
Neil