this "ボクを好きでいてくれ" really mean: "love me back" or "love me again"
the problem is...いてくれ　really means again? Or in what way affects the phrase.

Question

Answer

"Keep on loving me" might be the similar meaning.

「いてくれ」means "stay ~" or "keep on ~ing". 
For example:
Stay cool! クールでいてね！
Keep on singing until I fall asleep. 私が眠るまで歌っていてね。

Answer

You say "love me again"「もう一度、ボクを愛してくれ」when you realiseｄ that your girlfriend didn't  love you any more.

I hope you will love me forever「ボクをずっと好きでいてくれ」

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