Can this situation happen on Windows? From what I've seen, Windows code has no way of handling these random OpenClipboard failures. If it really works that way, it seems like a design flaw in the Windows API that we can't fix. It wouldn't be the first of those.
On Windows, we could fix this by running the tests on a separate desktop (assuming the software that's intefering doesn't follow us there), but that wouldn't help in Wine.