Some Kyrgyz say that Russians want to wait until more bloodshed is done in the country to achieve more sweeping results. They also say that Russians must have been involved in the recent outbreak of violence there. At the same time they state that the locals (Kyrgyz) would rather see Russian forces to intervene than the Chinese for instance (no one else can feasibly do so, apparently).
I’m inclined to agree with those who say that Russian intervention in Kyrgyzstan would be unpopular among the Russian public. The problem is that Russian public knows practically nothing about Central Asia. These countries have largely been ignored by the Russian media because of lack of interest and for political reasons. So it’s hard to prepare the public for intervention in a media-ignored region.
What is perhaps also very important is that there is no strong pro-Russian political group in Kyrgyzstan. Without strong, reliable local support Russian intervention may easily end up in military fiasco. Imagine for some reason the local opposing groups start taking on the Russian troops, it will be very hard to cope, given the terrain of the country, its remoteness, relatively large population etc. Perhaps the reason the Russians wait is also to reach a situation when everybody is so tired that they will really be glad to see Russian troops. In other words, the warring factions are still too strong (they have not been sufficiently weakened by the infighting) and some locals still hope they can handle the situation.
So given the information I know, it looks like combination of factors that explains the Russian (non)response.
And of course, the situation in Kyrgyzstan is likely to give yet another reason for the Russians to show off their vital importance to the U.S. I.e. the U.S. perhaps would be interested in having a more or less stable Kyrgyzstan, so the military base in Manas can operate properly. If Kyrgyzstan start to rely on Russians for its internal stability, it will effectively mean the U.S. increasing reliance on Russia. The U.S. is also unlikely to provide any coherent response to the situation in Kyrgyzstan and will not even try.