Of course, it can’t but being a dumbass never shuts some people’s mouths.
Neither House, during the Session of Congress, shall, without the Consent of the other, adjourn for more than three days, nor to any other Place than that in which the two Houses shall be sitting.
The House could vote to remain open during the entire year, and then not vote to allow the Senate to adjourn for more than 3 days, thus blocking the Senate from being in recess long enough for the President to make an appointment.
It would violate the "comity" between the bodies, where each has pretty much allowed the other to recess when they wanted. But it could be done, if they wanted.
Given that the GOP has 47 senators, they could block recess appointments easily, by making a blanket pledge to filibuster EVERY SINGLE NOMINEE if Obama does a recess appointment for a position where he hasn't submitted a nominee, or where the Senate Majority has refused to bring the candidate up for a vote.