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.
This isn't software. I needed to develop a mechanism to handle playing cards in an accurate and detailed way. After some testing of the minimum implementation, it became clear that the mechanism I had imagined was fundamentally too unreliable for use, so (using the lessons learned from the exploration) I developed a mechanism based on an entirely different principle.
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[ 1.9 ms ] story [ 11.0 ms ] threadI eventually gave up to avoid a headache.
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.