This is the 2248th most frequent Japanese word.
見逃す
To miss; to overlook; to let go.
In this sentence, 見逃す (minogasu) is used to express missing an event or an opportunity, specifically not being able to see the movie.
彼は映画を見逃した。
He missed the movie.
Here, 見逃す is applied to illustrate missing viewing these particular TV programs due to being occupied.
忙しくて番組をすべて見逃した。
I was so busy I missed all the programs.
In this context, 見逃す means to intentionally overlook or not point out someone's error.