There's a ton of series out there lately which are really well known as being awesome, but which have really boring or bad starts. I'm thinking Mass Effect (YOU SPEND LIKE A MILLION YEARS ON THE CITADEL!), Agents of Shield, Fringe (although I never got to the "I actually like Fringe now" point), stuff like that. How much time are you willing to sit getting through something like that, just under the pretense that you might wind up enjoying it later on, no guarantee (see: me with Fringe)?
I sat through three full seasons of Fringe before I realized that I just didn't like Fringe, so clearly my answer is "entirely too much."