Answer: I would be curious enough to dig the palm and inspect the root system and the planting hole. Even though you think all things are equal, you may find that the soil just isn't draining as well in that one spot as in the others. When you have it out of the ground, rinse the soil off the roots to inspect for insect damage or root rot (mushy roots). If you find nothing unusual, amend the soil with new organic matter and replant the tree. Water deeply to settle the soil after replanting. With any luck, the digging and replanting will be enough of a shock to prompt new growth in your palm.
Let's hope so!
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