I guess that is a good point, regarding the service life of the Enterprise A after STVI. There is no established time line between STVI and STVII. I think some things that would influence the Enterprise A's life span would be:
What was the stipulations in the the Khitomer accords, regarding ship building. Now for me I think the notion that Starfleet decommissioned all the constitution class star ships is total crap. Starfleet did not consider them "battlecrusiers" the Klingons did but their a war like race. Besides we see D-7/Kitinga class crusiers in the TNG. So what kind of deal was that? We have to give up ours but you can keep yours???
Nope really I see the Connies just being destroyed or slowly decommissioned as the front line ship as the Excelsior class replaced them as the "starship" class. So the A could have served on. Perhaps when the Ent B was commission they renamed the Ent A again?? Why not? Might have even gone back to its original name.