I had the exact same problem - fortunately one of my family members is staying at my previous address, so I could get my statements forwarded to me. Otherwise I'd probably also have gone to the opposition, though I've done that before (ABSA/Standard & FNB) - and they're all the same (as if there's a competition on about who can be a worse bank - at the moment I think ABSA's leading in that race, neck-n-neck with Standard).
After 8 years of trying to force them (NedBank) to change my address they finally gave in last November - they had to since it was because of a car loan I made through them: i.e. as adrianh mentions, sometimes their rules screw themselves!
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