Only a fan since 1992. I sometimes get sick of being a Leafs fan because I live in Germany and it doesn't make sense to follow a team that closely that plays at night on the other end of the world. But this would be the same if I was a fan of an other NHL team. Or maybe not.
I'm kind of the same cause I follow European football(Arsenal more specifically) I suppose it's easier my way cause the games are on in the morning as oppose to you where our games are on at damn near midnight over there.
But to the OP's question, Nah I'll never get sick of the Leafs; Some of the players, A different story. But it's what sports is about imo. The ups and the downs; And I know there's been more of the latter in the last decade, But it will make it all the more enjoyable when things finally do go well.
Besides if you or whoever were to quit now after how ever long you've been watching it would make it kind of pointless because we're actually starting to accrue a nice core of players who have loads of time growth ahead of them. We still could do with another piece here and there no doubt, But there are players to point to now that could be part of competitive team.