I adopted a Ponytail palm a few months ago in a healthy seeming condition. It has long (18-24") shoots coming from each of its three heads. I assumed that these were some sort of flower like you get with grasses. However, as these 'shoots' spring from the middle of the head there is nowhere for new leaves to sprout from. Old leaves are dying off at a slow but steady rate and so the foliage is beginning to look a bit thin. What should I do?

The plant stands 4' high (6' including the longest shoot) and is in a 10" diameter pot. I understand that I am not supposed to water too often as it is winter here in London and sunlight hours are short. The ends of the leaves are dried out and curled up.

Many thanks in advance for any advice.