Article One, section Five of the Constitution states:
Neither House, during the Session of Congress, shall, without the Consent of the other, adjourn for more than three days...
This presents a problem for President Obama, who claims to have just made a recess appointment when the Senate is not actually in recess. The Constitution says the Senate cannot recess for more than three days without the House's permission. The House has not granted permission, and as a result both houses have been holding pro forma sessions out of constitutional necessity.
There is an argument that pro-forma sessions are just a sham. Obama is not the first to make it. I don't find it very persuasive, but it's an argument that some very smart people make.
Yet in this particular case, in which the House has not consented to a Senate recess, the pro forma session does not seem to be the issue. The Constitution is the issue. Without the consent of the House to adjourn for more than three days, the Senate is in session, whether it wants to be or not.
The only argument left is one that the Obama administration has itself rejected -- that a three day "recess" is sufficient for such an appointment.