Well, kind of hard to diagnose without seeing the swing, but in general, the 3-wood off the ground is the shot that offers the least amount of leeway in terms of angle of attack. With a short iron, you can go anywhere from -2 to -10 degrees and do pretty well; with a driver you can go anywhere from -1 to +7 an do pretty well. But with a 3-wood off turf, you can only go about -3 to 0 and make it work. If you come at it steeper, there isn't much dynamic loft left unless you do something alien with the handle. If you go positive on the AOA...well, the ball is on the ground, so that won't work. Overall, there is just a smaller window of opportunity with that type of shot. I've never, ever heard a student say a low-lofted fairway wood off the ground is their favorite shot, and i think it comes down to the geometry of the situation.
That said, since you hit it well off the tee, there is a good chance you are fairly psoitive with AOA, which, based on a 2 for 1 sale, means you might also have too much of an inside path--which was mentioned by Brian. A way to check this is to understand why it goes low off the ground. If you smother the face to offset path or your low shots are thin, this is the right diagnosis. If your low shots are struck solid and start down the target line without hook, then the opposite is true: you are too steep.