Sounds like it may have little root rot

Dale is correct. This tree is dying from the top because of footrot. Now, the roots cannot sufficiently get water/nutrients that far. "George" wasn't looking very healthy last time you posted photos, a few weeks ago, and I should've said something. Sorry. -- Fix the problems below the soil line. Whether you plant it in pine bark/peat-based-potting soil mixture, or even coconut chips -- you must improve drainage. Also, make sure water drains freely away from the container and that it is not sitting in drainage water. Feel free to email me if you'd like more detailed instructions.

As to pruning back ahead of the browning, I do not recomend it. With citrus and most other trees, it's best to let them find their own way. They seem to have the ability to "know" just how much limb and leaf they can support and will die back just to that.
Also it seems to me from my experiance, that when you prune, the tree stops doing what it's doing to try to respond and live, and diverts it's energy to the cut instead. I don't have any real scientific evidance of that, it's only my observation.
Try to impropve the cause first. Let the browning parts go and only prune after the die back is completely dried out.
Arthur the Date Palm Guy

Thanks Arthur!!! that is just what I needed to know!! I have been trimming behind it.. With so few limbs left I didn't want to cut ahead of the browning.. but if it had been needed I'd rather have done what is best for the tree.. and only removed yellowed leaves so I could monitor weather it was stabilizing or not. So far only withered brown (shriveled) limbs have been cut off..
The browning doesn't seem to be growing at the rate it was before.. I hope this means that it is close to stopping..
Thanks again for answering my question..
Gina *BabyBlue*

Arthur has some valid points and obviously some experience in this area. But I think it's prudent to point out that dead and decaying tissues are best removed from a tree, to prevent fungus related problems.

AAE
I would agree IF you know that you have that sort of problem, like with fire blight in peaches, you would need to take appropriate measures. That would include pruning well back from the infection, sterilizing equipment after every cut, and burning the infected material. With that sort of problem there would be other signs, not just browning. This sort of problem is very rare in citrus and I have never heard of fire blight in citrus.
But the unanimous agreement of growers I know, all over So. Cal and in KY and TN, for all sorts of trees and also grapes, wait and let the tree or vine recover first. Then remove dead wood.

Arthur - Decaying growth is an invitation to a slew of problems. Dead wood is a different story. Decaying growth should not be allowed to remain on the tree, period.

AAE, I think that's what I said.
This question was about yellowing leaves and browning wood, not decaying wood.
Even in the case of decay though, it is not an absolute, it depends on what is causing the decay. In many cases pruning can do more harm than good.
Arthur the Date Palm Guy

Arthur - Did we look at the same pictures of 'George'? It was fairly clear to me that the browning was decaying. What else would be happening to the wood when the roots are rotting beneath the soil? LOL -- And I need to clarify what I wrote above about dead wood being a different story. Wood that has died (from being severed, pests, etc.) really needs to be removed as well.