... realizing that it will never work?
I tried having a normal conversation with a teenager the other day.
I eventually gave up to avoid a headache.
I have abandoned ideas during the investigatory phase because it turned out they weren't feasible, but I don't think that counts. The whole purpose of the investigatory phase is to determine if the idea is feasible.
Once begun, I can't remember ever abandoning a task because I realized it wouldn't work. I've certainly abandoned tasks for other reasons, though.
Answer this: _What_ was the last task about that you abandoned realizing that it will never work?