Prevent Excel from clearing copied data for pasting, after certain operations, without Office clipboard

The answer, unfortunately, is no, you can't stop this from happening.

As described by Joel Spolsky, developer and program manager for excel:

The official reason is that Excel doesn't really have cut and paste, it has move and copy. That's necessary because Excel automatically does reference fix up. For example, if cell A2 is defined as =A1, and you move cell A1 to A3, cell A2 will be updated to =A3.

If Excel actually cut things to the clipboard you would somehow need to have a reference pointing >into< the clipboard which is bizarre and for which there is no reasonable syntax. In other words, Excel doesn't want to leave you with dangling references during a move operation and isn't confident that it would be able to fix them up correctly when you completed the move by selecting "Paste."

Joel Spolsky 3/9/2004

source

What this means is that because of the difficulty inherent in the way excel maintains references, at the time of development there was no good way to store these references outside of excel and have them remain dynamic to be re-inserted. Once you change focus excel's ability to retain your original references is lost.

Unfortunately, MS does not consider this a bug.

You can try some clipboard manager applications such as Ditto, here is the link Ditto