Commentary for Taanit 51:21

When the gates close -- The Jerusalem Talmud, tractate Berachot, in the chapter [beginning with] "the morning prayer", defines when the "closing" occurs. One opinion is that it refers to the gates of the temple, and one opinion is that it refers to the gates of heaven, which are closed close to evening at the completion of prayers. And it was customary to add the Neilah prayer on all public fast days the same way we do on Yom Kippur.