In my opinion, stick with it. Making playoffs is bogus in a weak conference year after year and the cup run was a miracle on ice, however, you're a determined GM who evidently has passion and that's exactly what we need leading these teams. If your players are doubting you, work your ass off to show them reasons to believe in you - to not doubt you. Sit yourself down, look at your roster, assets and then look for a path for your organization to take and commit to it. It may lead you somewhere great, somewhere good or shit. Follow the path though. Get a vision and take the team there.
I do not think much great has come from your tenure aside from the one season. However, a fair amount of this is due to poor luck and maybe inexperience. I got a decent taste in a previous league, as well as 5 or so seasons in the VHLM prior to stepping up. If you enjoy GMing and think you can do good for the organization, why would you step down? There will always be people who criticize your moves, what you do, what you say etc. Don't take it personal. Ignore it if it's from the same old followers who tend to follow you, or learn if it's worthy of such.
You have a player who is unhappy and doubtful in your organization and leadership. You can give up and leave something you really enjoy and have passion for - OR, you can give him a reason to be happy and believe in your leadership. The jobs not easy, but your passion shows you're a good GM. I'd play for you!
I say take it up a notch, find a vision for the team and roll with it! Best of luck, mate