Conan did not lose his show, Jay did. Jays show is the one that tanked, and that's why NBC is canceling it. It did not get enough viewers, so he doesn't get to stay (your words). If Jay had any integrity he would just walk away and come back another day.
BTW - Conan would not be out after a few months as you say, he had a 2 year contract. It took Leno 3 years to finally get his show together and beat Letterman in the ratings.
Three points:
1) When Jay took over for Carson, his audience dipped sharply and after three months stabalized. Jay lost half of Carson's audience. but then he had his own rather respectible stable audience. After 5 months Jay's audience numbers were going UP, not down. And the Letterman show was the new kid on the block at the time. It started with tremendous numbers and started its slide. Conan's numbers were STILL dropping until last week. Had the numbers stabalized I would be with you.
2) Jay Leno Show got EXACTLY the audience NBC was expecting him to get. They also were in for the long haul to build Jay's audience. However, NBC's strategy was under fire by stations on the virge of mutiny. NBC figured they could make more money putting up a third rate (littereally third rated), cheap-to-produce show and having a smaller audience would still add up to more profits. And they were right. But the secondary effect it had on the local news broadcast ratings was totally overlooked!
3) Contracts in Television are based on keeping certain performance standards. "You have a 2 year contract provided thay you meet the following..... " If your show isn't holding its own, the network can cancel your show at the drop of a hat! Of course neither you or I have read the contract. But let's say the contract was hard and fast two year contract--- even if the total audience was 2 people in Peoria and no one else. NBC can buy out the contract and it would cost them less in the long run.
If you are looking for job security, Talent on a TV show isn't the industry you want to persue.