Not . . . at all is the double negative, οὐ μὴ [ou mē] , indicating there is no possibility of their ever needing to close. Shut is κλεισθῶσιν [kleisthōsin] , they would be locked . The same word describes the locking away of Satan in the bottomless pit (Rev. Rev. 20:3+). In the Millennial Kingdom, the gates of the earthly Jerusalem were never shut day or night (Isa. Isa. 60:11). Now, there is no night and the gates remain continually open. The gates remain open for those outside the city to freely enter into it, where God and the Lamb are in its midst, and where they may access the leaves of the tree of life. See commentary on Revelation 22:2.
no night there
The glory of God will provide a continuous source of light within the city. The text does not say there shall be no night, but there shall be no night therethat is, in the New Jerusalem. Whether night exists elsewhere on the earth is not said. Many assume there is no night anywhere on the earth as if the mere existence of darkness were an indication of sin.1 But the text only says there will be no night therein the neighborhood of the holy city and region of the earth which the Shekinah glory illuminates.
The city itself will radiate light as bright as daylight, so night will ever come, even when the earths rotation carries the city away from the sun.2Of course, we are in speculative territory supposing that the new earth is much like today: a sphere which rotates subject to physics as we know it today. The text tells us the barest minimum concerning many aspects of the new heaven and earth. They may be radically different from that which we assume from our experience today.
1 The existence of darkness was another result of the curse on the earth at Satans fall (Gen. Gen. 1:2). During the six days of creation, there was only a partial removal of the darkness (the sun by day) and the night (the moon and the stars provided limited light) that existed. But in the Eternal Order, since all the effects of sin are to be removed forever, there will be no night.Arnold G. Fruchtenbaum, The Footsteps of Messiah, rev ed. (Tustin, CA: Ariel Ministries, 2003), 538.