Hi Alan, sorry to hear that your palms are failing, well one at least. Of all the various problems that can cause palms to decline and ultimately die, water stress is the most common even without the type of severe water restrictions that you are experiencing right now. It is generally recognised that most palms are fairly tolerant of dry conditions but its a living organism and it has limits. Also we have to recognise that the soils we expect our plants be they trees or palms to grow in are often very far from adequate.
For us to be able to give you the most effective advice a bit more detail is required.
Do you know the species of palm that failed?
Are there other palms of the same species in similar location in your yard that are still ok?
In the palm that failed did you notice any discolouration inside the part of the stem at the point where it broke?
Generally other than water stress are there visible signs of other problems...ie, obvious yellowing of fronds well before they have aged, withering twisted crinkled frond growth soon after opening, yellow or dark blotches in the fronds themselves.
Are there any borer holes in the lower trunks of any of the palms, any jelly like substances oozing out?
Sorry to give you questions rather than answers but this additional info will help us to give you a more useful set of responses. Obviously a photo or two of your yard would be realy great esp of the health status of the palms.
To the question of what can be done to protect the remaining palms from the impact of severe water stress, well I'll attach a PDF from South East Water that has all the tips and info relevant for your needs.
Waterwise_Gardens.pdf