What a stupid question. There a multi-billion dollar company, why the hell would they give up. Ask is still one of the most well know brands on the web, so what i9f they only have and x% market share, thats still massive!
How much they pay people to search? Surely to god if there advertisers found out they where paying people to search they would pull out because there surfers there paying are not likely to buy any thing.
Yes, they should give up simply because Google is much better... and though Yahoo search is near horrendous, people still use it, and MSN just works. But... No, they won't give up simply because they are making money the way they are doing it and though there hopes of becoming the next Google are slim to none, its not like they'll just drop... thats like saying Wendy's should quite because more people go to McDonalds.
I don't think they should give up. Being ranked as the 4th biggest search engine on the net is a triumph on its own. What they need is an entirely new marketing strategy because what they're doing now isn't working that well.
I think they will not and should not give up. Yahoo and google are the best, and I dont like live.com, I feel ask.com still have chance. Go on!