Sounds like something is eating the roots of your palms, but I doubt it would be earwigs. Wouldn't hurt to get rid of them, though. Do you have gophers or voles in your area? I know for sure gophers will eat palm roots and usually go for your rarest specimens.

We do live next to a walnut orchard. And in the past we have had gophers. No sign of them this year. Perhaps this is damage from the previous year? I had to rip them out due the severity of damage. What can I do to save my other palms?

People I know with gopher problems plant their palms in gopher cages -- kind of a chicken wire-like enclosure for the roots. Another method which involves more work, but can be easy if you have a lot of rocks on your property -- when planting, line the rootball with fist-size or larger stones. So you dig your planting hole a bit wider and deeper than necessary, put a layer of rock in the bottom, set in your palm. Then stack rocks around the rootball and fill in with soil outside the rocks. When the gopher hits the rocks, it just goes another direction, leaving your palm untouched. As the palm grows, the roots will eventually push through the rocks, but by then you have a nice big palm.

Thank you very much! I honestly would never have thought of such an easy, yet ingenious idea! Wish me luck on round two!