None of Suffolk’s post offices will be closing under an efficiency plan announced by the U.S. Postal Service on Friday. he post offices in Chuckatuck and other Suffolk areas had their retail hours cut this fall, to the ire of many local residents and business owners. However, the Chuckatuck station now is open 24 hours a day for post office box access, Sansone said. An upgraded security system had to be installed before the lobby could be open around the clock.