Since the picture was taken in 1920 it would have seemed to have excaped that fate during World War I.
World War II is a possibility during the scrape drives of that era. However, right now I am more inclined to believe that it was washed in the Arkansas River by the massive Mississippi and Arkansas River valley floods of 1927. During those floods the Arkansas River cut several new channels. One of which eradicated the remains of Fort Hindman and most of the original Arkansas Post. That event was only 7 years after the cannon was displayed in the picture.
Arkansas Post in 1920 was a semi official state historical site, and I assume that officials just accepted the lose of this relic because of the massive damage created by these floods everywhere else. Probably no attempt was ever made to recover this Cannon at all if this is what really happen to it.