Two big factors in the decision to decommission 1701-A would probably stem from the damage suffered during the battle over Khitomer and the age of the vessel.
In The Search for Spock the original Enterprise was to be decommissioned after "20 years of service"1. At this time the Enterprise had sustained considerable damage from the battle with Khan in the Mutara nebula, which more than likely played a large role in that determination.
SCOTT: With all appreciation, sir, I'd prefer to supervise the refit of Enterprise.
MORROW: I'm afraid that won't be necessary.
SCOTT: But, sir...
MORROW: I'm sorry, Mister Scott, but there will be no refit.
KIRK: Admiral, I don't understand. The Enterprise is not...
MORROW: Jim, the Enterprise is twenty years old. We feel her day is over.
SULU: Admiral, what's going to happen to the Enterprise?
KIRK: She's to be decommissioned.
CHEKOV: Will we get another ship?
At this time the refit Enterprise was only about 10 years old, with The Motion Picture taking place in the mid-2270s and The Search for Spock occurring in 2285. This leads one to believe that, despite a substantial overhaul, the age of the underlying space-frame may also be a determining factor on when to retire a ship.
Now lets consider the USS Yorktown. Assuming that the USS Yorktown referenced in The Voyage Home is the same one that was rebranded as 1701-A it is likely that the ship was on its original post-refit shakedown cruise when it was disabled by the probe. This would account for why so many systems were still inoperable at the start of The Final Frontier, as secondary systems like fully functional turbolifts and transporters wouldn't be needed for a cruise around the block. If we assume that the original vessel was built around the same time as the Enterprise, it would still have a space-frame pushing on 20+ years by that time.
Moving on to the The Undiscovered Country, Kirk and team were three months from retirement when the movie started. The ship itself was 7-8 years into its refit life, nearly as long as 1701 was when it was to be decommissioned. It took heavy damage from Chang's ship during the fight, with substantial destruction being wrought upon the saucer section. One shot even fully penetrated the saucer from bottom to top.
So we can then imagine the discussion that might have happened when the fleet admirals reviewed the ship upon Kirk's return:
Kirk has wrecked another ship.
What do we do with it?
Fleet Command is trying to get Kirk to retire. Considering the damage and age of the vessel let's decommission his ship as well, to hurry him along.
1: Although Admiral Morrow says the Enterprise is 20 years old, it had to have been older, since Kirk's five year mission started in 2265. If you add on Pike's stint of command on the Enterprise, possibly with another 5 year mission, then the space-frame was at least 25 years old, likely older. While there are no on screen sources nailing down a construction date, several "official" off screen sources list the date of launch being 2245, which would make the Enterprise 40 years old at the start of The Search for Spock. It should be safe to assume that the USS Yorktown would have a comparable launch date.