Posted: 28/02/2012 at 13:39
It sounds like either cold, overwatering, or a combination of the two. Beaucarnea comes from Mexico, so doesn't like our cool, damp winters, especially if sited in a place with limited sunlight. However, they are quite robust plants, and I've seen one that was frosted outside, resprout the following spring when brought into warmer conditions.
I advise that you stop watering altogether and leave the plant to go completely dry. If you see any signs of squishiness in the branches, then cut them back by 2-3 inches. If possible, move the plant to a warmer place (though as the weather is warming up now, that may not be necessary), such as a sunny conservatory. My plant goes to my neighbour's in winter as I don't have a conservatory. In April, start watering again on a fortnightly basis and hopefully you'll see some new shoots appear. Good luck!