Even the nursery they were purchased from wont help? That's strange, usually they'll give advice.
Have you looked into your county ag extension? Sometimes local colleges and universities will partner with county agriculture departments to offer "free" services to the local citizenry. They can also help with disease identification because that can have wide range impact. As an example, I tried growing to fig trees in my front yard and had a lot of problems getting them to leaf properly and grow. I called up the UofA ag extension here in town and they actually sent someone out my way a few days later. He looked at the fig trees and told me to just pull them up and get rid of them. When I inquired why he told that they had contracted a local mosaic virus that is very common to the soils around Tucson and that they were essentially a lost cause. I stuck with them for over two years trying every thing I knew and, like he said, they just eventually withered and died. He was nice enough about it and he told me, if I wanted figs, to grow them in deep pots and use soil that was sanitized. The local soil is just no good.
So, if 2 out 3 are ok, it may just be a sickly Palm. Problem is, if it has a disease, then you need to get it out before it spreads to the others.
