As far as I know (German is my native language) there is no common phrase like that. You would say “(die) Tage vergingen” or “Tage und Nächte vergingen”.
My guess is that Brecht is referring to the “Nacht” in a metaphorical sense.
Ich empfinde es außerdem noch so, dass die Nacht durch Singular zum etwas viel Urweltlicheren und Standhafteren wird. Bertolt Brecht habe ich leider noch nie gelesen, aber den Satz finde ich umwerfend schön!
As this is from one of Brecht’s moments of levity, he will have used the singular simply for the sake of scanning, I fear. (But the metaphorical and/or Urweltlicheren und Standhafteren explanations are brilliant.)
It is from a song, so the rhythm has to be right, the metre of the line has to fit the rest of the text. I can’t remember the melody, though, and so cannot swear to it that all is well on the poetry front.