Indeed, it's difficult to see how our heroes could have maintained phaser contact with the Scimitar, which was cloaked for the most part, maneuvered quite a lot, and was firing back so hard that the heroes had to maneuver, too. Most of the shots fired by the E-E were "ranging shots" anyway, attempts at establishing where the invisible enemy was, and any sustaining there would have meant wasted energy.
Ok, so if they were trying to establish where the Scimitar was, why didn't they fire phasers at 1 percent or less of total yield for a second at a time? They could fire a whole lot more often, and when they made a hit the computer would note the location and possibly even calculate the velocity and direction of travel of the Scimitar and calculate where it was likely to be in the next few seconds. You could then follow up with torpedos and full power phaser strikes. I know the Scimitar maneuvered a lot, but assuming it doesn't maneuver like a fighter you'd think the computer would be able to track reasonably well.