Only if you changed whatever they declined your link for (PS. Its against the FAQ/Rules to hand add a signature so you may want to refrain from that in your posts )
I usualy dont aprove sites that rewsubmit .... only in special cases they changed content etc etc so i gues it's useless maybe thye only exception is Dmoz i will resubmit untill i get in
After six months is a good rule. Give the editor long enough to forget their initial bad impression, and give yourself some time to improve your actual site. Usually if your site is rejected there is a good reason. If you haven't figured out what that reason is yet, it's almost certain your site isn't a good fit for the directory, and you are wasting your time.
Often when a site is rejected by a directory, they are told not to resubmit. I certainly wouldn't bother to resubmit unless you have a good idea why you were rejected in the first place, and have taken some sort of corrective measures.