Your ancestor had gone home several months earlier and was not at Arkansas Post. The ink on the date July 1862 reads as clear as you'll ever see on a Confederate discharge form. Do you not have a copy?
Another reason for discharge in the summer of 1862 -- he gave his age as the reason for discharge. At that time he was thirty-five, and Congress had recently passed a law requiring men up to age thirty-five to serve. By 1863 the age limit had been raised, so he could not have gotten out of service at a later date.