You can keep zucchini bread at room temperature in an airtight bag or container for up to 3 days. If it's not gone after 3 days, place it in the fridge, where it will keep for another week. If you know you won't be eating it right away, wrap it in plastic wrap and place it in a freezer bag, and place it in the freezer, where it will keep for at least 2 months.