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So I think it depends. If the probability stays at the same rate after trying each time, then you should quit. Like lottery ticket example that Eliezer gave is an example to that. But if there is an improvement, even if it's slight, then maybe keep trying it? It may be tricky, because every time you can say "but there is still a chance right" ? If you plot the events on a model like Markov chain, then it could be easier to be rational.
It may be because we are evolutionarily wired to be curious about our surroundings so that we could feel 'safe', so if something is known, then that may mean that is 'safe', if something isn't known then there may be a 'danger' there. Just a thought.
I wrote a song. Here's the link. https://soundcloud.com/azeems-jukebox/azeems-jukebox-myndbreyting