Hockey's assertion is not exactly correct. Sometimes a FA will "consider," rather than "reject," less than he is asking for, especially if you are just offering fewer years, or if you are offering just a few percent less than the request. This is only applicable during the primary open FA period; at all other times the FA will automatically reject these offers.
If the FA outright rejects an inadequate offer-- if you get an "X"-- he will never look at that offer again. But if you get another indicator beside his name, and/or if the offer met his demands but you aren't leading, you just got outbid and can bid again.