I worked for a silk screen company years ago and we normally reused the screens to save costs. The stencil was water based, kind of like a gel so I doubt you could save them too long as they would become brittle. In fact sometimes a stencil piece would flake off and we would repair with a water based goo and a small brush. At the end of a run the paint would be cleaned with Ketone. Then the cleaned screen would be set in a tub and water power washed to remove the stencil. We did save a few screens for a few years for repeat runs like "Virginia is for Lovers" but in the 70's we mostly used a photographic stencil maker so you could just reshoot a new one and not tie up the screen and frame.