Some other app is likely monitoring the clipboard (such as my own ClipMate) for updates. Since the clipboard is a shared resource, any app that touches the clipboard needs to be careful about expecting it to be available, immediately after updating it. For example, if an app modifies the clipboard, and then tries to open it again right away, it should be prepared to deal with the scenario where other apps have opened it for inspection/pasting.
Excel has historically been bad about that. 15 years ago, the error would have said "out of memory", but it's really the same thing. The programmers did not anticipate that anything would go wrong, so they throw up a generic error and quit, rather than devise a defensive catch-and-retry strategy. Oh well.
Anyway, my advice for the end-user is to press ESCape to un-highlight any cell after copying. That will relive Excel of its obsession of clearing the clipboard, so it shouldn't even try to clear the clipboard when you drag it around.