But the issue is that ships in DS9 large battles behaved in such a fashion as if shields were non-existent and that their hulls were on 10% of structural integrity at all times.
It was artistic license I'll grant you that ... but ended up incredibly dumb-ed down for the sake of 'cool' factor and drama.
Some of those battles did last for hours, though. Say, for Operation: Return, we saw the Defiant join two lowly Miranda-class vessels (the Sitak and the Majestic). Later on, we see the same two ships escorting the Defiant, but then getting destroyed with a few shots.
Since a time span of a few hours elapsed between the start of the battle and the destruction of those ships, I'm going to have to say that it's perfectly logical that those ships took a heavy amount of fire before biting it (and yes, the way they were both destroyed was pretty cool, at least for a Trek show).