Another factor was that after the fall of Vicksburg there really wasn't much of a need on the part of the Confederacy to hold onto the Arkansas River valley unless you wished to use this area as a springboard for operations into Missouri. President Davis wrote of this need to Kirby Smith in the fall of 1863. But it wasn't going to happen. Bruce Catton points out the importance of holding Arkansas in the summer of 1862 to the Confederacy and the command problems this presented in the opening segments of his book "Never call Retreat". That is why the lost of the garrison at the battle of Arkansas Post hurt the Confederate efforts so much.
As I understand the Confederate "Battle Plan", even as early as May of 1862 under Hindman, was to force the Union army to have to fight through a series of fortified defences before they even got to Little Rock. In other word Bleed them to death before they ever get there. The one thing that the Confederate Commanders seemed to lack was that they did not have an aggressive mentality. They seemed to think of everything in a defensive perspective. Fixed fortifications without proper and aggressive mobile support can always be flanked by manuvers, or reduced by superior firepower.