Ok. The answer has been found. We are only allowed nine (9) homescreens and when all are filled up the iPhone will drop the ability to add additional homescreen icons. If all of your homescreens are filled and you try to add another iPhone app, it will be added to iTunes but it won't be added to your iPhone until you make room for it.
That explains why I could not add a new web page icon to my homescreen. I deleted one of my icons and replaced it with the new web page icon.