For me, the more I financially/mentally/emotionally invested in the Washington Capitals--which, I have to regularly remind myself, is one cog in a massive business owned by billionaires (and a game played by millionaire professionals)--the more the organization's losses became, like, my own personal losses. For a while, I tried to distance myself from the entire experience--which was made a little easier with every soul-crushing post-season loss. I've recently tried to re-evaluate what it means for me, personally, to be a fan of this team: What I put into it, what I get out of it, how much of that experience is a positive thing in my life (entertainment, exhilaration, the joy of a shared experience), and how much of it is a negative (stress, frustration, moodiness, obsessiveness, argumentativeness, etc.) I'm finally at a place where I can enjoy the successes but not be consumed by the losses. It took a while to get there, but it's been working for me.
This is just my own personal experience, and is not meant as advice for anyone else or any kind of judgement of other fans' experience.