Probably seven years. Banks are legally required to keep them available for that duration so I imagine most of them figure if they have them, they might as well make them available because sending out paper reproductions is expensive.
One caveat, this isn't to say that all 7 years are immediately available, as that would be pretty expensive from an infrastructure perspective. There will probably be a point at which they have to be retrieved and then cached for online presentment. At WaMu this takes about 24 hours and happens for statements older than 18 months.
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