^ an icon with a generic image and an icon with an application-specific image. I think you should be able to catch it now.
The OP presents the problem that he sees only a generic icon for the Acronis software shortcut, that being the shortcut for trueimage.exe. He has circled the actual trueimage.exe in the Acronis program folder which is also generic, which he calls as "damaged". The link is still functional. Only the specific image is lost. If you now read my post I think you should be able to make sense of it, if I had really made it non-sense. May be
I had not simulated the fault condition in my screen shot. It is only illustrative of the procedure.
If I were able to simulate the fault condition presented by the OP, the shortcut will be a generic icon and the first icon in the "Select an icon from the list below" will also be a generic icon as that is what is there in the program folder - the source as per his screenshot. (whichever the shortcut refers to. Forget whether it refers to truemage.exe or trueimagelauncher.exe. I just checked that both launch the same screen in True Image Home 2011 and the shortcut it had put on my desktop links to trueimagelauncher.exe)
That said, I routinely find a few desktop icons losing their specific image every now and then. I just follow the above procedure and find the application-specific icon is the first icon in the list and selected automatically. I double click the icon or click on OK but nothing happens. Repeat it a second time and the shortcut icon regains its original image. This is not a big or troublesome issue and so I have not bothered to find a permanent solution. If someday, sometime I stumble upon a permanent solution, I will implement it then.