I drink 8 oz of grapefruit juice every day. Will this destroy the enamel on my teeth? If so, should I stop drinking this juice?

Not recommended. Acidic drinks erode and soften tooth enamel. Drinking something acidic, like grapefruit juice, then rinse your mouth and wait 30 minutes before brushing your teeth, since you can actually brush the acidity deeper into your teeth and get cavities. Moderation is the key.
Drinking juices. If you drink it within a short period of time, it not too bad. Sipping acidic liquids over a long time is bad! Consider substitutes that are not as acidic at least part of the time and Vitamin C tablets. Rather than guess, see your own dentist to determine the condition of your teeth and whether or not this has and will have an effect on your enamel.
Add water. Rinse mouth with water immediately after drinking grapefruit juice to minimize the damage the acid would do to the teeth. A single mouthful of water helps rebalance the pH and shortens the time to neutralize the acid effects.
May be. All acidic solution can dissolve enamel and patients suffering from bolemia can damage their teeth! Stomach acid is hydrochloric acid which much more potent than the weak citric acid. Just rinse your teeth with water after your fruit juice will eliminate the problem which is small to begin with!
Don't drink juice. Its preferable to eat the fruit with its fiber intact than to drink juices with concentrated fructose. Blending fruits is ok but its best to avoid fruit juices in preference to whole fruits.