I suspect there is more to the OP's thought process than just the state championship ring.
Without knowing the details, I'm not one to pass judgment. Maybe he's in a program where he is not receiving support from the school, community or parents. Maybe he's constantly having players he has developed for years poached away by other schools. Maybe he's worn out from busting his butt, and not getting the results.
I realize the OP was focused on the state championship issue - but perhaps that's just a part of the equation.
How about framing it this way - Despite best efforts to create a winning program, when is it time to throw your hands up and walk away? What would make you say, I can't take any more?
Then there is another thing to consider... If you are not truly happy where you are coaching, are you doing the program a disservice by staying? If you come to the point where you can no longer put your heart into the team, wouldn't they be better off if you moved on? If you don't love the program and going out and coaching it every day, there is no way it will ever get your best effort.
It doesn't mean you are a bad coach or a bad person, just that you no longer have the passion that the program needs. As long as you can be self aware enough to realize this is the case, I think stepping aside is not only an option - it is the correct option.