I wrote a test program which I attached the VS2010 files for.  It demonstrates the problems I'm seeing with these two issues:
https://www.nevron.com/Forum/9186/AutoHide-tabs-hidden-from-loaded-DockingFrameworkState
https://www.nevron.com/Forum/9156/NDockingPanelTabInfoIndex-not-referenced-on-auto-hidden-panel

When launching the program it lists the steps to follow to see these two issues.  My program is seeing these two issues and I'd appreciate any advice on how to fix them.

Hello Craig,

Thank you for the example application.

We are working on solving this problem. 
We will let you know when we find a solution.

Best Regards,
Nevron Support Team

Hello Craig,

Today we have released a service pack which includes the fix of the bug you described.
Now saved state of the autohide panels should be loaded correctly.

Regarding icons on the docking panels, they are not part of the docking framework state which is persisted. You will need to set them back again when the state is loaded.

Best Regards,
Nevron Support Team

Thank you for fixing the tab visibility problem in the 15.6.18.12 build.  It seems to be working fine for me.

You wrote, "Regarding icons on the docking panels, they are not part of the docking framework state which is persisted. You will need to set them back again when the state is loaded."  I do understand this and the sample program I provided is doing this during the "LoadLayout_StateRestored()" method in the code I provided.  I know this is working as I see the icons on the tabs when I toggle the auto hide.  Is there something else I need to do to make this work after the state is loaded?

Also, in testing just now I noticed the tab order is reversed from what I saved them at.  Here are updated instructions when launching the previously attached program which explains how to see both of these issues:

1) Press AutoHide button on "One" panel
2) Press Save button (which saves .xml file to program folder)
3) Press Load button
4) Notice auto hide tab icons are missing (bug???)
5) Hover mouse over "One" tab to show the panel
6) Press "Toggle Auto Hide" button on "One" panel to keep it open
7) Notice the tab order is "three, two, one" instead of "one, two, three" when I saved it (bug???)

Thanks for the tip regarding using the UnregisterDockPanel method.  I wasn't aware of the need to call this method.  I searched the documentation, examples, and the forum and only found one forum reference that mentioned it.  It might be good to change one of the example programs to use it so people can become aware of the need to call it.  I could not tell if it mattered but I call this method before I dispose of the panel.  If the order is important please let me know.

I downloaded the 15.7.10.12 build today and noticed it doesn't include the fixes for the icon and the tab order you said would be part of the next service pack.  Will this service pack be included in a build I can download soon?