Depends on a lot of factors like:
Is it a torsion bow, where the staves don't bend, the tension being in wound up ox sinew or the like?
If a tension bow, is it wood stave? Metal Stave?
Is the string a string, a cord of gut, a wire, braided wire?
Is it a sturdy, heavy trigger mechanism, a light, hair trigger one?
In the ideal scenario, where it's a tension bow, with a metal stave, using braided metal cable and a sturdy metal mechanical trigger. . .then likely it can sit under tension for a long, long time. . .like years or decades long.
If it's a torsion bow, or a wood stave, with a wooden trigger mechanism using a gut string, then likely it'll stretch the string out over lengthy periods at cock, or the bow will lose it's spring over longer time. . .or a carved wooden peg mechanism or delivate mechanical trigger might just give up and break.
It's one of those "GM can call it as they choose" scenarios, since there's a great amount of variety in crossbow construction.
