That sort of relies on Geordi staring over at the shield frequency indicator the entire time.
At the very least any console that shows the ships shield frequency. And a quick glance is all that is needed. LaForge's VISOR see's most everything, so glance and enhance and boom shields might as well be down.
Anyway, another time the ENT-D fell short to me was in Yesterday's Enterprise. That was the battleship Enterprise-D and it still shot only one burst of torpedoes the entire fight and something like 4 phaser shots before going under.
And since they were trying to defend the ENT-C from multiple attackers, that would've been an ideal situation to do a saucer sep.
That version of the ship also suffered from a severe case of exploding consol.
Saucer separation might not be available on the Klingon-War-Universe type Galaxy Class ship. There was a mention of damage to "structural latching system", but if that is the latching between the star drive and the saucer is unknown. Besides even if it could separate, they might have needed the power from the saucer's impulse engines.