I totally agree with the lunge line idea. You need to build your confidence!
Balance has a lot to do with body position, leg position, core strength, and leg strength. Two of the biggest things that will cause you to lose your balance and tip forward are looking down at your horse and letting your legs slip too far back. You'll find that those two parts of your body have a huge effect on your overall position and security; when your head is down and your legs are back, your whole body pitches forward. When your body is forward, one little stumble can offset your balance even more and possibly land you on the ground.
So. Focus on looking up and ahead to where you're going. If you're on a circle such as on a lunge line, keep your body moving in the direction of the circle but don't let yourself lean and look in to the circle. Ride with your chin up as if you have confidence, and you'll end up with real confidence! As for your leg, keep your calf slightly behind the girth at all times and think of hugging your horse with your legs. You shouldn't be gripping with your knees, but there should be no gap between your legs and the horse. Keep your heels down to help anchor you and think of lining your body up ear/shoulder/hip/ankle. Above all, have confidence! You've been riding for a long time and you know what to do, your fear is just getting in the way of memory and performance.
To build your leg and core strength, gradually work in 5-10 minutes of stirrup-free riding every time you ride. I know it's scary at first, but you have to trust yourself! Start out just on the longe line walking and keeping your legs in the same line up as you would with stirrups, but slightly longer. Don't just let your legs dangle or you'll end up slipping and feeling insecure when you trot and canter or when your horse spooks. Gradually work up to sitting and posting trot without stirrups (excellent for the core, inner legs, balance, and stamina!). You'll be pretty sore after your first few rides, but it'll be worth it in the end! Who knows - with all the confidence you'll gain, you could be galloping around the pastures in no time