I'm not terribly familiar with the code to add icons for iOS (and Android) when you select "Add to Home Screen", but I used the following, based on what I read:
<link rel="apple-touch-icon-precomposed" href="http://www.redtypewriter.com/wp-content/uploads/2014/03/57.jpg"/>
<link rel="apple-touch-icon-precomposed" sizes="72x72" href="http://www.redtypewriter.com/wp-content/uploads/2014/03/72.jpg"/>
<link rel="apple-touch-icon-precomposed" sizes="114x114" href="http://www.redtypewriter.com/wp-content/uploads/2014/03/114.jpg"/>
The code seems to work, but after I add it to my home screen, after some time, the icon disappears and I'm left with a black square in place of the icon? What's happening? The site is: http://www.redtypewriter.com/ if you want to take a look, and I am using a custom WordPress theme.
Thanks!
There are two mains reasons to get black icons:
In your case, this is because your pictures are in JPG format instead of PNG.
With you original pictures, I observed three issues:
As soon as I converted them to PNG and change the HTML code accordingly, all issues were fixed at once.
In addition, you don't define enough pictures. For example, your icon won't look great on a Retina iPad.