i have no c lue what to say right here.
the elite four is allways possible to be challenged no matter how many times you beat them .
and after you have defeated them the first time you may go to kanto and once you beat all kanto gym leaders the elite four goes into "second round" and the pokemon they are using will be at a higher level and much tougher .
for more info and my source : http://www.serebii.net/heartgoldsoulsilver/elitefour.shtml
Yes you can battle the elite 4 as much as you want