If you refrigerate the Ezekiel Bread the Ezekiel bread will be good for up to 14 days or two weeks in fridge before going bad and growing mold.
When you keep the Ezekiel Bread out on the counter it will last for up to 5 days before growing mold so by refrigerating the Ezekiel Bread it will last longer.
Or if you really want to make sure the bread lasts for a lot longer you can and should freeze the Ezekiel Bread if you're not gonna eat it within 2 weeks.
When you freeze the Ezekiel Bread it will last for up to a year in the freezer and that's what most stores and bakeries do with the Ezekiel Bread is they freeze it to make it last longer and stay fresher and to prevent mold growth.
Ezekiel Bread freezes and thaws pretty good without going stale like some other breads.