Question: What's the longest you are willing to work on something before you give up and admit defeat

Leo Garcia answered on 14 Jun 2010:

Some people spend almost all their PhD’s working on something that doesn’t work in the end! However, we can learn a great deal through failure as well as success – and although not many scientists like publishing negative results (eg. “we tried doing this, and it didn’t work!”), it is still a perfectly valid contribution to knowledge.

So to answer your question – I would continue until I had learnt something about why it wasn’t working, and move on from there!