But that doesn't really make sense according to a plain language reading of the Constitution, which says: "The President shall have Power to fill up all Vacancies that may happen during the Recess of the Senate, by granting Commissions which shall expire at the End of their next Session." 

The Constitution appears to define "session" as whenever Congress is meeting; i.e., until its next recess. This is consistent with the only other usage of "recess" in the Constitution, which says that if Senate vacancies occur while state legislatures are in recess, the governor can make a temporary appointment "until the next meeting of the Legislature." 

The Constitution writes about Congress as if it can be in only one of two states: "in session" or "in recess." By definition, then, a recess comes between sessions and a session comes between recesses. So, a recess appointment should only last until the end of the next time Congress is in session, which will be from the end of the Fourth of July recess until the end of the August recess (i.e., in September). 

I'd like to hear what a Constitutional expert would say about this reading of the Constitution. Also, I assume that past practice has been that recess appointments last until the end of the next official session. But that's not what the Constitution says, in my lay opinion.