Matt nailed it when he explained that trying too hard can start to ruin your draw. You have to trust your tip to do what it's going to do and that the ball will back up. Relax.
I'd characterize it more as a spin/speed ratio problem, which comes up against the maximum level of precision you can execute your stroke at. The important thing to remember about that is:
"You don't know what you don't know."
Plenty of people who are great with mid-range draw suddenly get just end up with dead and spinning CBs when they try to load up on power for long range draw shots. Sources of this problem are all in stroke execution.
Problem #1 you're pulling your cue off line when you try to over-power it. This is one of the most common mistakes and also very hard to self-diagnose because the crazy thing is you'll still pocket the ball just like you intended but not get the draw. Why? If you push your cue left just before contact the CB jumps off to the right but with unintended left spin. Even though you pushed the CB right by a tiny fraction and should miss with an unexpected tiny left cut, the left spin will throw the OB a few degrees right, still hitting the pocket. An instructor especially one who is video taping you can help you identify if this is the problem.
Also note that while it may sound counter-intuitive, it helps a lot to practice these shots on faster tables. Your goal in practicing on a fast table is not to make it easier to draw the ball but to see your mistakes more clearly. If you're routinely pulling your stroke and getting unwanted sidespin, the CB will more obviously slide to the side you're missing to before it draws back. Harder to detect on slow cloth.
Problem #2 comes from jarring the cue forward when you transition on your front stroke. Especially if you have a 'lively' cue and you are trying to violently accelerate, the tip WILL oscillate from the shock of the acceleration and a tip that has a slight buzzing movement at contact will not grip the ball as well, sacrificing spin. There's a reason snooker tapers draw well with some of the most violent cue acceleration, but in pool people are better served with a longer backswing and working on mechanics to get an even delivery that is not twitchy. Pro tapers can make the front end of the shaft vibrate as they are accelerated through a curve (nobody moves their cue in a perfect line back-to-front).
Problem #3 can come, depending on circumstances, from hitting too low. Just like hitting too hard, you can begin to hit too low, even below what you might have thought the miscue limit to be. Getting your tip too near the table can start to get you cuing low enough where you're now wasting a lot of power on spin and not acting enough on the center mass of the CB to launch the CB forward. Also you can start to lose grip (and thus spin) before you reach the miscue limit, although this gray area between the start of a miscue and 'maximum spin' on the CB is going to be different based on your tip, cue weight, and stroke characteristics. Also at the lowest extremes, any tiny mistakes with the tip striking slightly left or right of your aim point will again bleed power from both backspin and forward momentum.
Problem #4 AND problem #5. These happen together a lot. A problem when you go for more power than you're used to (even if you manage to keep the rest of the stroke in line) is that you're probably going to bridge longer than usual and frequently not get as close to the ball at address. It's hard to take your normal PSR, prepare for a big stroke, and still get your tip as close to whitey as you should have it on every shot. If you let your shoulder drop too early or jerk your shoulder into the shot you're probably going to get a lot of tip rise and hit much higher on the ball than you thought. It's just as bad if you still hit the right point on the ball but have any see-saw motion right at contact. The tip needs to drive straight into the ball for maximum grip, spin, energy transfer. If your tip is starting to wander up it's not purely striking into the ball at impact but is also moving up the surface of the CB. Absolute spin killer, and if you're moving on the shot, as we all know, all bets are off.
CURVE
Curve comes form using the things you usually want to avoid on a big draw to your advantage... either off-center hits or intentionally added sidespin. The shape of the curve is highly dependent on table conditions so don't worry if the CB isn't dancing as pretty as exhibition shots you see on newly-felted TV tables, as long as you can still force the delay of the curve to where you need it and end up where you want to. Of course any mld-angle cut with very high backspin starts to move off the natural angle and the bend backwards. Force-follows are a little harder to show that dramatic curve except at more narrow angles.
Perhaps counter-intuitively) you can make the CB slide out a bit longer before the curve of the follow catches by helping yourself with some inside spin. Even where you're dead-straight, you can aim your CB a fraction from a full-face hit and then add inside spin to still throw the ball on-target. Even when you have a little angle to work with, inside spin can help generate a little extra friction between the CB and OB so the CB sticks behind it a little bit longer, halting some of its natural momentum and encouraging it to slide off on the stun angle before the front-spin takes. All of the combinations you can go through to make a force-follow pause and curve the way you want it are crazy, but it's certainly worth experimenting with it once you have the confidence in your stroke .