The battery may be faulty. Although the key is not designed to be opened - it is possible to open it and replace the battery. You can get one (Panasonic VL2020 3v) for a few quid. Here's a post with pics on how to do it (requires some soldering). Definitely worth a go before splashing out on a replacement key.

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Cheers, Brian

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2001 X5 4.4i Sport
Black Sapphire, Hi Gloss Shadowline, Full Privacy Glass.
Too Cool for Jack Bauer