Because even admitting that there is a rebellion going on in Chechnya -still, after so many years- would prove his claims that Chechnya is under control and the military operation has been a success to be wrong. It's easy for him to justify a military operation which has been intensified with the pretext of fighting Chechen terrorism on Russia if acts of terrorism committed by Chechen rebels have disappeared.
Then he can say "ok, folks: We sent even more troops down there, but as you can see, the situation is under control now, and those Chechens are no longer a threat, thanks to me. Your sons are there for a good purpose, i.e. to solve the Chechnya conflict by military means."
But all of a sudden, Chechen terrorism escalates - now how does that look? Wouldn't mothers, fathers, wives & girlfriends say: "Hey, Mr. President! You said that our men were risking their lives in Chechnya for a good reason and that everything is under control now. But it seems like your oh-so-glorious military operation was a total failure - we don't see less terror, we see more! The situation seems to be further away from being under control than ever!" (remember PMB's questions, btw!)
What's the solution? The ongoing rebellion must be denied, and at the same time some legitimation for giving even more power to the military and the secret service, as well as even more severe censorship of the media (which is always good if you want to stay in power) must be found - the perfect role for evil Al-Qaeda terrorists!
But as I said, I fear that by calling them he might get what he's calling for eventually, just like it happened in Iraq.
The solution... yes, that's difficult. What's most difficult is that every step forwards into chaos and terrorism requires at least five steps backwards to make it undone, and not even on a linear scale... the efforts needed to reverse the trend are increasing with every step that's made in the wrong direction. Look at Northern Ireland: The situation there is still tense, and that's centuries after the English started to settle there and fight the Irish, starting this conflict that lasts till today.
Some factors that favour a relative (albeit fragile) peace there are moderate living standards (no hunger, no dramatic poverty), that it's right in the middle of Europe, where many countries have a watchful eye on it, and that it's being reigned by a kind of democratic government and even has some particular regional privileges that enable both sides to cope with conflicts in a peaceful way. There are moderate leaders like Gerry Adams who are tolerated by the English government. And last but not least, the educational standard is fairly good.
In Chechnya, how much of this applies? But Putin will not be in power forever, and who says that his laws (which lead more and more towards a dictatorship with democratic façade) will not be reversed one day by a future government? After all, it's the first time for centuries that Russia has a "democratic" constitution... the first time Germany had one lasted roughly 20 years and ended in WW II... and Germany is right in the middle of Europe and a very "governable" country... it's small in size, has a good infrastructure and pretty nice living standards. Besides, it has no long tradition as a unified (and thus, centralized) country - unlike Russia! Thus, the odds that our second democratic experience will be longer and more peaceful are good. But in Russia, things are a bit different, especially in the remote provinces. Russia is hard to govern, and its history is one of long centralism and autoritary regimes. I don't expect any significant progress during Putin's presidency, and even afterwards, it might take decades.
Peace is slow... you can push it a bit, of course. But so far the West remains rather silent... which brings us back to the pipeline thing: Where do these pipelines pump their oil?
Bingo. (again, see Pierre's remarks)
Oh, btw - enough spaces?