Almost never. I think my pearl (which I got after diamond) is the only game after 2nd gen that I have ever restarted. Most of the time I would sooner buy a new Pokemon game then restart an old one. I get extremely paranoid about not wanting to delete anything that may have some value, even though my old games are usually stripped dry when I migrate to a new game.
Please check out my blog/guide to competitive pokemon at pkmntrainercory.blogspot.com