You navigation order is based on the order you have set in your Navigation View. If the changes have not yet reflected on your pages on your live site, try running a full site publish. That should update your live sites content.
If you are not seeing the changes in CM1 after changing the navigation order in your Navigation View please submit a technical support ticket through our support portal.
I click on the navigation option, brings up navigation of my site. Then click on whichever section i want to work on. Once it drops down, I proceed to click once and drag into alpha order.
I was able to reproduce the issue. So what I discovered is when you make the change your navigation it will save once you leave the Navigation View but if you simply minimize a level then expand it again the changes will not save.
So to make your navigation changes, leave the Navigation view after you rearrange your sections then go back to Navigation and see if the changes are saved.