Out-of-universe, shields in ST (or, really, any other sci-fi universe) last precisely as long as the plot requires, and not a nanosecond more. If it builds tension, Worf can shout about the shields being down to 58% after a sustained volley lasting half the episode; if it gives us impressive visuals or shows that the characters on other ships are in peril, the (now-ex) tactical officer can simply forget to raise the shields altogether. (Pretty, though!)
In-universe, you have to realize that we almost never see an unbroken shot of even a single ship going from pristine condition and full energy reserves to glowing cloud of plasma. Our view bounces from ship-to-ship, from exterior to interior and back again -- and even when the ships aren't on our television screens there's still a war being fought. You may have only seen that ship over there take one or two phaser hits before it exploded, but in the realities of war those could have been the fiftieth and fifty-first hits this battle, to say nothing of yet-unrepaired damage it may have suffered in previous engagements.
(Edit to add: There's also numerous occasions where we see weapons fire but do not see where it winds up, such as phaser blasts and photon torpedoes flashing across a viewscreen, but without a corresponding sound or shutter indicating the ship whose view we're sharing was hit. Sure, many of these could simply be misses ("Evasive maneuvers!" and all that), but equally many could hit and damage ships we later see exploding.)
Further, there really is a mis-match in ship classes in many of these engagements -- Jem'Hadar fighters, for example, simply don't have the size to even carry shield systems powerful enough to counter the multiple phaser banks of, say, a Constitution-class starship -- each individual bank dwarfing the size of the fighter! Ships such as these are only a threat due to their numbers, as is mentioned several times throughout these episodes.
All this on top of what BBlake points out, that during most of the shows we're following Starfleet's greatest achievements in master shipbuilding -- but in a war there will be everything from today's greatest pinnacle of tech to slag heaps that were obsolete last century. Especially if it's a war you've been losing, where you're having to pull out every last resource you can muster just to survive one more day against insurmountable odds. (Just ask Poland, who tried to resist the German armored division's Blitzkrieg with cavalry -- and yes, I do mean the man-riding-a-horse kind!)
And, finally, you can't forget the point James Sheridan also makes above, which is that the Dominion did have a technological edge, so it only makes sense that their ships (and, perhaps to a lesser extent, those of their allies) would have less trouble punching through even the best shields going up against them.