There can be numerous reasons why a plum tree drops its fruit before it ripens: insects, disease, high winds, and stress ( too much water, too little water, lack of nutrients, poor drainage, weed competition, and excessive shade, for example). But the most common reason -- especially when, as you say the tree is heavily laden -- is that the tree has produced more fruit than it can support. If this happens again, you'll want to thin the fruit. I realize that removing perfectly healthy fruit from a tree goes against everything a gardener believes! But getting rid of the excess ensures that a good crop of nice-size plums will stay on the tree until maturity. Think of it in the same way as you might thinning radishes that were sown too thickly.
When the fruit reaches about 3/4-inch in diameter, pick off extra plums so that the ones that remain are about 4 or 5 inches apart.
Also, whenever you've had insect or disease damage around fruit trees, always rake up and remove from the area any debris (old leaves, etc.) from the ground. This helps break the cycle.