"couldn't" is a past tense of "can't." Then shouldn't it be "knew" not "know"? Is it common grammar error that natives make?
You are correct! Unfortunately, this is a common grammatical error amongst native English speakers. Most English speakers don't worry about small grammatical errors when they are speaking, so you might hear small errors every once in a while. It should be "I couldn't sleep last night because I knew that it was over between us." Here is an explanation of the differences between can't and couldn't just to ensure understanding. Can't is a contraction of cannot. Cannot means that currently, this person is unable to do something. Ex: I cannot whistle very well. Ex: She cannot swim very well. Couldn't is a contraction of could not. Unlike cannot, couldn't is past tense. It means that in the past, someone was unable to do something, but may be able to do it now. Ex: I couldn't swim until I took swimming lessons. Ex: I couldn't go to the bar until I turned 21.