I've done some digging. While this won't help for all time.
If someone deletes or declines a friend request. You can't send another request for a year. If they really don't want to hear from you. They can block requests permanently.
So, while you can't see a list of closed requests. If you have the option of sending a request. You at least know that person hasn't declined within the last year.
I don't think that it's unreasonable to send a request once a year. If they really don't want to hear from you they can ignore it once a year or block you permanently.
Learn how to delete a friend request on Facebook.
www.facebook.com