The most common reason for zucchini breadand other quick breads (and cakes) to collapse as they cool is the ingredients are too vigorously or quickly mixed, which incorporates lots of less stable air bubbles into the batter. As the bread or cake cooks, those air bubbles make it rise, but because they are unstable, the bread or cake then collapses as it sits.
Try mixing with a gentler touch: use medium, not high, speed on the electric mixer. Add eggs one at a time, mixing slowly in between each addition. After the final ingredients are added, stir or mix only until just blended (again: do not over-mix).
Recipe: Zucchini-Pecan Flaxseed Bread