My question is: Since 'sakuban' ( 昨晩 ) is already used to refer to "last night", why is tthe word 'yoru' ( 夜 ) for "night" still used in this sentence?
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夜[yoru]/朝[asa]/昼[hiru]の○時 is used like a kind of set phrase, e.g., 夜の11時 "11:00 pm," 朝の7時 "7:00 am," 昼の12時 "12:00 pm."
By th way, 昨晩 would be read as ゆうべ in this case, since 眠れなかったんだ is a colloquial expression. さくばん tends to be used in formal situation.
e.g.
昨晩、首相は退陣を表明しました。[Sakuban, shushou wa taijin o hyoumeishimashita.]
Last night, the prime minister announced the resignation of his cabinet.