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.

I tried having a normal conversation with a teenager the other day.

I eventually gave up to avoid a headache.