The expression I'm familiar with is " will be the death of me". Assuming this means the same, I don't interpret it quite as you suggest. To me, it means that his frustration at not being able to solve it will cause his death (not meant literally), or at least his attempts to solve it will be overtaken by death.
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Angliholicthe death of mehttp://www.macmillandictionary.com/dictionary/british/death