Wanted to add:
I was told the grass is St. Agustine / Palmetto.
Not sure if that is true.

How long ago was the second sodding? St. Augustine sod, by it very nature, spreads by runners and some of those rooted runners will get cut when the sod is machine cut. Without roots, the unrooted portions will die, leaving an unhealthy look when in fact, the remaining rooted grass is still growing and probably healthy.
Was the soil base amended or worked over before you laid the sod? Minimal shallow tilling helps the minimal root system of the newly cut sod penetrate the existing soil base. Adding some organic matter also helps but isn't absolutely necessary.
Did you roll or otherwise press the new sod into good contact with the existing soil base immediately after planting (simply walking on it lightly will do the same thing for such small areas)? This is almost a necessity... Remember that cut sod only has a minimal root system remaining after being cut so even though you say you are watering daily, the water may not remain in or near the root system long enough to do much good.
As a trial only and because of the small area, you might try a one time application of root stimulator by watering can or other means. It certainly won't hurt and might give the viable grass a boost.
Steve

Even though the area is small, did you consider a soil test? Also, if the sod is new, watering once a day in the hot Florida sun will not allow it to root. The idea is to keep the roots moist for at least 2 weeks then back of to daily and a couple of weeks after that, 1 good soaking a week.

How much water are you using every morning?

Normally with new sod you should water three times per day (morning, noon, and early evening) just long enough to moisten the sod and the very tip layer of soil underneath. For an area that small you could run a soaker hose over it and leave it running constantly at a very small drip. By small I'm talking less than one cup per minute out of the faucet - maybe 1/2 cup per minute.