Assuming these e-statements are for consumer accounts and further assuming they include EFTs of one type or another, Reg. E requires a minimum retention period of 24 months. If you have to maintain them in a manner that will allow retrieval for bank examiners, why not leave them where your depositors can get to them also? If you decide on something less than 24 months, don't forget that taxpaying customers may need access to a full year's statements in order to retrieve evidence of deductible items.
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...gone fishing.