On February 3, 2012, Admiral Vladimir Vysotskiy, the Commander-in-Chief of the Russian Navy announced that the Russian strategic submarines will resume regular patrols "on the 1st of July or a bit later." According to Vysotskiy, the Navy was awaiting this "for 26 years."
What this probably means is that Russia will try to keep at least one strategic submarine at sea at any given time. I'm not sure what will change in June 2012 that would allow the navy to do that - the only significant development is that Novomoskovsk will probably return to service by then - it has been in overhaul since May 2011. But then there is Ekaterinburg, which is unlikely to be back after the fire until at least 2014. Also, another submarine, Karelia is in the dry dock right now, although this seems to be a brief repair work (let's hope they removed missiles this time).
Maybe the plan is to rely on the first Project 955 class submarine, Yuri Dolgorukiy, which is expected to begin service some time in June-July 2012. That's a possibility, I guess.
It's interesting to look back 26 years to see why Vysotskiy believes it was such a remarkable year. It wasn't in fact - according to the U.S. naval intelligence data (posted by Hans Kristensen), in 1986 Soviet strategic submarines conducted about 80 patrols. But the patrol rate was higher before and did not drop significantly until much later - there were still 60 patrols in 1990.
In 2008, Russian strategic submarines conducted ten patrols, but as Hans notes in his post, these were probably clustered together rather than spread over the course of the year. Still, that rate seems to indicate that the Russian Navy could keep continuous deterrence patrols with five or six submarines.