Not necessarily unheard of. The last Essex-class aircraft carrier, the USS Philippine Sea, was commissioned in 1946 and decommissioned in 1958 after serving a short 12 years. The 1701-A could've been the last Connie ordered and have a shorter career than her older sister ships.
Sure, I can accept that reasoning. It's just that I find it unusual that Starfleet decided to build one more Connie in just the three months between the destruction of the original Enterprise and the end of STIV, and coincidentally have it ready for Kirk and crew at the conclusion of their trial. I think it would make more sense for them to have just found an old ship and changed the name and registry.
In offscreen sources like
Mr. Scott's Guide to the Enterprise, it was postulated that the starship that was eventually designated the
Enterprise-A was in fact finished, construction-wise, months prior to the Cetacean Probe's arrival at Earth.
The USS
Ti-Ho (NCC-1798) had been undergoing its initial deep-space trials and had just returned to Spacedock when the Probe showed up -- it was after Admiral Kirk's trial that it was rechristened NCC-1701-A, but it had been completed some time around
Star Trek III.
Non-filmic, of course, but very plausibly laid out in that book; it's always been a particular favorite of mine.
Generations was a mess of plotholes- everything from "Why aren't Lursa and B'eTor dead yet" all the way up to the end of the film and it's shameless "fire when cloaked" ripoff from Star Trek VI.
To be sure, it's not the same thing that we saw in
Star Trek VI -- in that film, the
Enterprise-A used sensor devices to track the gaseous emissions of Chang's Bird-of-Prey in order to gain a targeting lock (the ship was utterly untraceable up to that point).
In
Generations, the
Enterprise-D triggers a cloaking-activation via transmitted signal-pulse in order to force the Duras sisters' ship to drop its shields long enough to score some damage; the ship was already decloaked and well-visible to the
Enterprise.