Well, you can also say that he stepped down only after assassination of his opponent was not successful …
you can also quote Pres B who said that he will only step down by the direct message from Almighty… Did he receive such a message? I think we believe that there are no non-Jewish naviim after Bilam, is it a firm position or just a dig at other religions? Maybe one of his Jewish subordinates or relatives got the message? Or maybe he got an indirect hint from Almighty (he is smart than the Gadol of his site!). Maybe it took him a couple of weeks to realize that his debate performance was such a message … or poll results are also a message.