Les,

To maintain the temperature of food that's already cold you want larger pieces of ice, not cubes. Block ice is preferred.

Even better is refilling disposable soda/water/gatorade bottles with water and freezing them -- just squeeze out about 10% of the water after filling to allow room for expansion as they freeze. Since the melt water is contained within the bottle your food doesn't get wet and the temperature at the bottom of the cooler stays closer to freezing.

Ice cubes are good for rapidly cooling things down, but big chunks of ice are ideal for maintaining temperature.

I also use those rectangular blocks of gel that do the same thing as refilled bottles but are more space efficient. When I'm on an extended car-camping trip I rotate them into my Engel 12V fridge set for freeze mode and can go indefinitely.