The Russians have declared their red line, 'no taking of Armenian sovereign land'. So long as Azerbaijan sticks to only taking back its territory, it'll be in the clear.
The writing is on the wall, the Armenians are a burden for Russia right now, which is why the Russians haven't intervened yet, even though the status quo benefits them. The Armenians will either lose, or the international community will convince Azerbaijan to stop its offensive, in either case, the Russians have nothing to gain.
The hope for Russia now is that Azeri land goes back to Azerbaijan, and Armenia remains in one piece. In this way, their south border will become stable again. They'll still have influence in Armenia, but they know now that Azerbaijan is a lost cause for them. Their goal will be to counter Turkish influence in Azerbaijan, by propping up Armenia even further, after the war ends.
[Edit]: on a side note, I wouldn't be surprised if Azerbaijan and Turkey have Washington's secret backing. Keep in mind, Turkey is a member of NATO, and Azerbaijan shares a border with both Russia and Iran. Azerbaijan is also geographically close to China, making it an ideal place for NATO to counter Russia, Iran and China. It also helps that Russia, Iran and China are all rivals to both Turkey and the US.