Some sentences for 気がつく are translated as “didn’t realize”. Why is the conjugation 気がついていなかった instead of きがつかなかった? Meanwhile other sentences with the translation “realized” use 気がついた.
Is this because lack of realization is an ongoing state but realization is just a single event?
Yes you are right 
気が付いている is a state, can be translated to “being aware” etc.
気が付いていない is also a state, “being ignorant” etc.
Can you think of any situation where 気がつかなかった would be appropriate?
急いでいたからスーツがラーメンで汚れていたことに気がつかなかった。
Because I was in hurry, I didn’t notice my suit got dirty with ramen.
ｗｗｗｗ、はなもとにあるメガネに気が付かなかった。
Lol, I didn’t notice that I had glasses on my nose.
Etc, in some moment in past you didn’t notice something.
If you want to put emphasis on living for a while without noticing something use 気がついていなかった .
長い間 隣に住んでいた人が有名な俳優だなんて、私は何年も気づいてなかった。
I haven’t noticed for years that my long time neighbor was a famous actor.
**BUT, the Japanese themselves don’t really care about that nuance in case of きがつく, so **
長い間 隣に住んでいた人が有名な俳優だなんて、私は何年も気がつかなかった。 Will work as well.
In other words you can use 気がつかなかった in both cases. What is more きがつかなかった will seem more natural to Japanese speakers.