A Chechen terrorist in the woods (photo taken in summer 2009)
The question of whether Moscow is losing the war on terror in the Caucasus appears to have been prompted by the rising number of acts of terrorism and the number of fatalities in these acts in the North Caucasus republics, especially in Dagestan and, recently, in Kabardino-Balkaria. Some of these acts, like the recent suicide attack by three jihadists on the Chechen Parliament, were quite spectacular.
The short answer to the above question is that Moscow cannot lose the war on terror in the North Caucasus because that war simply cannot be won by the opposing side. In Chechnya, the mujahedin, the separatists, the Islamists, or whatever else you might call them, once did win a war against the federal center, and what happened? The separatists could not build a proper state and were only able to exist a few short years as a bandit republic, an assemblage of warlords with their private, clan-based armies engaged in various criminal activities such as hostage-taking, slave-trading, production of counterfeit money, and so on. They were aided and abetted by radical Islamists in other Muslim countries and those forces that viewed instability in the Caucasus as a lever to keep Russia in its place, and still they failed.