Term for a television event that causes you to be awake during sleeping hours

Well, not easy to find a single word. What you are looking for could be described as

unmissable:

An unmissable film, play, etc. is so good that it must be seen:

• Critics are describing the musical as "unmissable".

But the notion of time (during the night) is not included and must be expressed by a context which will show that this is a live broadcast during the night. To use a term offered in one of the comments, you could say an unmissable all-nighter.

Another phrase that might tempt you, though it is not a single word, is

keep your eyes glued to something

If you say that someone keeps their eyes glued to something, you mean that they are watching it with all their attention. (Collins)

Another variant is keep someone glued to the screen. See this title on the odyssey site:

11 Movie Recommendations That Will Keep You Glued To The Screen

So you could say that

This all-night broadcast keeps people glued to the screen. (Such shows are also called overnight broadcasts)

They are "burning the midnight oil.....meaning to read or work late into the night (https://www.google.com/search?client=firefox-b-d&q=burning+the+midnight+oil+meaning)