The most common complaint that I hear about foxtails on the Keys is that they require heavy heavy feeding. Without it they display the symptoms that you mentioned. I would suggest probably at least 5-6 times per year using slightly smaller amounts per application. Now is the right time to start for this year. If you can, try to get 12-4-14 to get a bit more potassium. BE SURE to get a good quality fert ($$) that have the minors as well. I'd bet this would help. Good luck.

seems like frost damage... often palms get burned but the damage starts being visible weeks later when weather warms up. cold hardy potted palms are notorious for getting winter damage because even with low temperatures the pot freezes and the plant is unable to provide enough water to the leaves when they receive direct sunlight. washingtonias and cycas revoluta are notorious for getting these burns. i always covered my potted palms or moved them to a shadier spot in winter if there are extreme temperature swings or alot of sunlight exposure with a frozen root ball. check these pictures Note the tips of those washingtonia that look dried are similar to your trachycarpus palms. just make sure the spear ( where the new folded leafs come out of the stem) is intact and robust. trachycarpus can get 50 % leaf burn and easily survive.. i've had trachycarpus of a few years old that completely lost all their leaves and survived as long the spear is intact and as long the spear doesn't have any fungal infection they are fine. yours have around 10 % maybe 20 % burn that is nothing to worry about. cut away all dried and damaged foliage but don't cut into the green foliage. if they weren't in pot but in full ground they probably wouldn't have this damage. also remember that these palms are very cold hardy..

It's a while since I've been down that way. Went with friends from Auckland to a party (in my young and wreckless days), think we were in Tairua, can't remember exactly. If you're on the coast on sandy soil you're likely to have nutritional problems. Sandy soil doesn't hold plant nutrients well. You need to keep adding a lot of compost/organic matter to it. The humus is good at retaining nutrients.

Photos aren't showing up. Is this a Bismarckia nobilis?