Several years ago, the leaves on one of our red oak tree's limbs began
to lose their color and eventually fell off. Now the condition has spread to
a dozen or so limbs. I've been told that a leaf shredder pest is
responsible. If this is true, how do I break the cycle?

Best way to safely get unwanted bugs off your tree is a good shot of garlic/pepper tea. The Garlic is systemic which means the scent will be present all through the tree. The scent puts off most bugs, even if it's too faint for you to smell. The pepper will discourage any bug foolish enough to go ahead and try biting in.

I'd also apply the sick tree treatment to boost the tree's overall health and therefore boost its natural immunity.

Naturally all of this works best when used in the overall organic program.