My interpretation (because these are all just interpretations): The 1701 was going to be decommissioned in III due to damage, time in service, and possibly some PR related to the fact that part of a *cadet crew* had been killed aboard her. The Enterprise-A was a new construction slapped together from spare Connie parts in a hurry, which is why she was in the state she was in at the beginning of V. Connies were still being built, refit, serviced, etc, but were no longer the top of the line ship for the fleet. Given the damage sustained in Star Trek VI and the additional time that had passed, the -A required refurbishment, and the designation U.S.S. Enterprise was reassigned to the -B, once again for PR reasons. (Starfleet seems to care a lot about PR, at least in the movies.) The -A, however, kept the name Enterprise - UES Enterprise - and was transferred to the Sol System Defense force. She was used for regular patrols of the system and anti-piracy actions up until "Best of Both Worlds" when she was sent to join the fleet meeting the Borg cube that was, after all, headed for Earth - so that was still well within her mission profile. And she was destroyed there.
That's why we rarely if ever see Connies in TNG - they've been apportioned out to planetary defense forces in the Federation, or even loaned/sold to allied powers or private research groups.
