The Broadway revival of “Private Lives,” starring Kim Cattrall, will shutter five weeks earlier than producers had originally intended, with a new closing date set for Dec. 31.Producers cited the show’s middling performance at the box office as the reason for pulling the plug. “Ticket sales have been slower than we had hoped for and it would be irresponsible to continue running into the notoriously difficult January period,” said producer Paul Elliott in a statement. Helmed by Richard Eyre and co-starring Canuck thesp Paul Gross, “Private Lives” earned strong reviews when it opened Nov. 17 but never quite caught on at the box office. Production’s highest weekly tally so far came in at around $380,000. Last week the play saw sales decline to about $325,000, in a frame when the majority of Main Stem productions were on the rise. Attendance came in at 55%. By closing early, production avoids the post-New Year’s sales slump that traditionally hits Broadway in January, when the tide of seasonal tourism subsides. The Broadway outing reps the third leg of the Cattrall-toplined staging of the Noel Coward comedy. Production preemed on the West End in 2010 and earlier this year played Toronto prior to its Rialto stint. Originally skedded to end its limited Broadway run Feb. 5, “Private Lives” is produced in Gotham by Duncan C. Weldon, Elliott, Theater Royal Bath, Terri and Timothy Childs, Sonia Friedman Prods. and David Mirvish.