I've seen the behavior of icons changing on desktop shortcuts too... except mine are related to shortcuts that point to targets that are not connected to the computer yet since my VPN connection has not started yet.
Once you have a connection to the internet, does selecting the desktop and pressing F5 help?
I think the misunderstanding is becoming clear. Your 3 desktop icons are all shortcuts to programs in Windows Explorer. I don't have a problem with the PROGRAM icons which are stable. The problem is with SITE icons (i.e. icons that point to a url) in which the type of file is designated "Internet Shortcut" pointing to a specific url like http://google.com. I have a mixture of both types on my desktop.
BTW starting today, the icons fixed themselves. No doubt they will revert back to generic in a few days, but for now they are working (It's interesting that the Amazon shortcut was stable while the other two turned generic for a while.):
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