Very strange. The only things I can think of that might cause that are something wrong in the roots on the affected side or some type of weed killer that may have drifted or been sprayed on part of the fronds. These are both long shots but I have never heard of such symptoms on a palm.
I would also suggest you contact your County Extension Office (3695 Lake Drive; Cocoa, FL 32926; (321) 633-1702). They may be able to look at a frond or better yet a photo of the plant and assist you with diagnosing the specific cause of the problem and by recommending appropriate action to fix it.
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