When will you give up a niche website?

If I kind of knew the niche wasn't profitable (but still wanted to give it a try) and after some months the performance is as poor as expected, then I move on. If I know (from research) that a niche is profitable, I don't give up, even if it takes years.

Diversification is always key. Don't count your chickens before they hatch. And also each site you administer is slightly different. Variety of factors such as niche, trending topics, Seo, changes in Google algorithm etc will make a huge difference.

So you shouldn't give up a site unless it is an actual dead topic. But there is an audience for everyone out there. The trick is to keep trying and if you're smart enough and learned enough you can make a huge impression.