Here's my suggestion on how this could be implemented in-game.
An Arty mission is called in as normal and goes to FFE. After it completes or is cancelled, a "REPEAT last fire mission" button appears for that battery/gun/mortar below the other mission types (point, area, linear) If the unit is on-board and performs any other orders (move, fire, face, etc.), comes under any level of suppression or loses C2, the REPEAT button goes away. Otherwise, the REPEAT button remains active for X number of turns (amount X depending on the level of support; for example Battalion 81mm mortars might be able to REPEAT for 9-10 turns while Corps 155mm Howitzers only can REPEAT for 5 turns) The X number could appear on the button to help the player remember how long this command is available? If calling a REPEAT, the FO does not have to have LOS to the target; it fires with the same accuracy as the previous mission. If the REPEAT button is selected, all of the mission parameters (type, duration, number of tubes, etc.) from that unit's previous mission are re-used and cannot be modified until the mission is in FFE. (this should reduce the potential "gamey" use of quick missions to register a target then blanket it with an emergency barrage later in the game.) If adjustments are called in, normal spotting rules (including LOS and any delays) are back in effect. If the REPEAT button is selected, the mission parameters are displayed along with the normal target indicators. If the REPEAT button is clicked but the fire mission not confirmed, then it's just like any other arty request that isn't confirmed and nothing happens. Once the REPEAT mission is in FFE, it's treated like a normal fire mission and can be cancelled, adjusted or REPEATed.