A poorly Torbay (Cordyline) Palm
 

We have a 14 year old, 20' Cordyline Australis (I think!) in our south facing garden in Torquay, Devon. It has four brown telegraph pole type trunks sprouting from the base of a similar height and one 2' trunk in the middle.
The leaves are leathery and sharp and about 4"/6" wide at the base, mid green in colour. This year all the leaves from the tall trunks turned yellow and then brown. They have all fallen off and the tips of the trunk look slightly whithered with just an old flower pod hanging from each. The small trunk in the middle seems OK.
Help! Could someone please tell me what has happened and what I should do next. Should I leave it, feed it, cut down the tall trunks? It is such a shame because it is a lovely palm. My neighbour's palm is thriving so I don't think it's the weather.

Many thanks