I would leave the Cocos put, in hopes that one day it will take off.

The coconut is climatically challenged. It appears to barely make up in summer what it loses over winter. They can sometimes do better when tall than when small. So it could be worthwhile to try and get some sort of protective cover for cold nights. That way you stand a better chance of getting the crown growing up away from the cold lower layers of air.

Not sure why it wouldnt do well. The winter was mild in Florida this year so I don't think that would be the reason. The coconut palms I saw in Orlando a few weeks back already had a decent batch of fruit on them which says a lot coming out of winter.
I think it has to do with the soil, there is something going on that it doesn't like. I would get a new one and plant it in a different spot, but definitely keep that one because you never know when it will take off. I would probably just cut off the brown parts so it looks like it's a little happier because there is a lot of nice and green foliage on it! The ones I have seen in some parts of the Bahamas look a lot like yours so I bet the problem with those is the same as yours.
Good luck! Great pics, I love that date palm!
-Alex

I've grown all types of coconuts and the yellow Malaysian does not do very well here. They need lots of fertilizer with micronutrients in it 3-4 times a year.
The green Malaysians do much better here.
I have 2 that are a cross between a Jamaican tall and green malaysian.
Very vigorous in its growing habits, very thick trunk and huge fronds.
The coconuts are the biggest I've seen.
I just planted 10 from seed and 2 have sprouted so far.
Good luck!
Kevin

I think you coco is getting too much shade. The grass looks a bit sparse too.