Comment by kazinator

I just found that the Vim manual recommends, right in the doc for backupext, the use of the BufWritePre hook instead, so:

  :au BufWritePre * let &backupext=("." . strftime("%y-%m-%d.%H:%M:%S"))

This has the right effect that every time you save with :w, a new backup is made of the previous contents.