If you are working with a faculty letter writer, it is common practice for them to keep letters for this exact situation: not having to recreate an entire letter for you if it is needed later on. If you're dealing with an employer/extracurricular activity/etc., it's probably a good idea to ask them to keep it in case you need it for a future date. Needless to say, you need to have these letters dated. It would raise some flags if you didn't.