Great things are done under extreme pressure
"Is there a time to give up"
I have mixed views on the topic, someone asked me after a session with the boys, "don't you ever feel like giving up" he had overheard some of the conversation I had earlier with my engineering manager on the difficulties we had over the last year, nearly a complete re-design of the product and the qualification hurdles we have and that we still did not have a product fit for the market we were targeting. I said of course I do, who wouldn’t when you feel like you are peeling an onion and each time you peel a leaf back you find another “bad” one, another set of issues to tackle, but I said if we had stopped a year ago on the this we would not have developed the new software or the hardware, we wouldn’t have developed the new manufacturing processes and improved the yield, so there are times that giving up is not the correct answer, but there are times when you have to be honest to the stake and share holders that “this dog is not going hunting” for the market you invested in us for , but ( if you are luck and have positioned the company correctly) we can tackle this market which has a similar growth profile and you will still see a healthy exit. I must admit there are more “mongrels” out there than “hunting dogs”, and when you are leading a company you need to keep scoping out the future and adjusting the internal strategy, the key is to do this with thought causing an internal confusion about objectives and diluting the focus, but that is why you are paid the big bucks or should hire me.
So to answer the Question posed there are times when you should give up, but not until you have pushed every avenue you can to make it a success, great things are done, when people are under great pressure, ask you Grand parents or Great Grand parents.