The worst example was in Generations. The Enterprise was getting its ass handed to it by a rundown Bird of Prey, and their only return fire was a single phaser shot. They were too busy talking about plasma coils.
This of course was the height of ridiculousness. Riker fires one shot at an obsolete BOP whose shields probably aren't operating at maximum efficiency. Then Riker, after 7 seasons of being brilliant and strong, does pretty much everything else he can wrong and is only saved by a combo of Worf's obscure knowledge and Data's ability on how to use it.
Depending on the power of the weapon firing on it, shield longevity is variable. If it's some podunk ship with low powered weapons, sure the shields can hold all day long. But, as we've seen in many instances, if they are hit enough with strong weapons, they'll eventually collapse.
It's like a WWII battleship with heavy armor. If you fire at it with machine guns and other low caliber weapons, you may cause superficial damage and kill anyone exposed to it, but you can fire for years and you're not going to penetrate the armor around it's most vulnerable parts. But if you're another battleship with 16 inch guns, you may not hit it on the first or second shot in a fatal way, but eventually if you keep firing you're going to pierce it's armor and destroy or sink your opponent.
Riker's first order should to have been to open up with everything possible and keep firing until the shield collapse and then blast those a holes to hell. It may nave taken a minute or so, but it would have happened soon. Plus while the BOP was taking all of these hits with it's shields up the impact of the Enterprise fire would have been shaking the living hell out of the BOP possibly causing systems to fail and making it very difficult to accurately target the Enterprise.
But no Riker became an idiot and turned profile, exposing a much larger target and then showed the warp engines as he ran away and the Enterprise D was lost as a result.