The primary reason that Beauregard was not retained as head of the Army of Mississippi derived from Davis's deep personal dislike (which some have described as a hatred) of him.
Although Beauregard was a capable combat commander and engineer, his strongly expressed contrary opinions often clashed with Davis, resulting in poor relations between the pair, which can be traced back to the fall of 1861.
Beauregard's controversial decisions to retreat from Shiloh, and later Corinth, all fed into Davis's animus towards him. Think the final straw came when Corinth was abandoned, and Beauregard took medical leave without seeking permission beforehand, causing Davis to remove him from command when the Army retreated to Tupelo. Davis's explanation for the removal was that Beauregard had technically deserted his post while on an unauthorized sick leave. Beauregard's supporters claimed this was a guise for Davis's hatred of Beauregard (see 'Autumn of Glory' by Thomas Connelly, at page 33).
Despite an ensuing petition presented to Davis by some Richmond politicians to reinstate him in Sept. of that same year, Davis had no intention of re-appointing Beauregard to Army command.