Lots of ranking systems can see you drop below an inactive player when you lose (Elo for one). It doesn't mean the person below is definitively better but the loser could always challenge (the person they slid beneath) to earn their spot back. I think having to win your way back into a rematch makes more sense than a loser being able to initiate a rematch against the same defending after a week.
Ultimately, there's going to be pros and cons with any permutation of this kind of set up (delays between matches and/or playing the same people regularly and/or being challenged by people well below you, etc). It's a matter of picking your poison so to speak
I just think that if someone challenges another player, they should have some risk involved as well... which came to my mind especially when considering your idea of potentially allowing people to challenge multiple rungs above them. Otherwise, if #6 wants to challenge #3, then #3 has nothing to gain and #6 has nothing to lose. At the very least, #6 should be at risk of dropping a spot. Now, if #6 wins, do they simply swap positions? That would be highly volatile.
A simple method:
A loss = move down one spot regardless
A win against lower opponent = no change (but ideally there's a cap to number of defending matches in a row)
A win against high opponent = move up one spot