Some extensions seem to interfere with the icons of others...

If you would like to do a little troubleshooting, you could disable all nonessential or unrecognized extensions on the Add-ons page. Either:

• Ctrl+Shift+a
• orange Firefox button (or Tools menu) > Add-ons

In the left column, click Extensions. Then, if in doubt, disable.

Usually a link will appear above at least one disabled extension to restart Firefox. You can complete your work on the tab and click one of the links as the last step.

Does that stabilize the Navigation Bar?

To get comments on your specific extensions, please post a list. You can extract the list from the Troubleshooting Information page. Either:

• Help > Troubleshooting Information
• type or paste about:support in the address bar and press Enter

At the upper left you should see a button that says "Copy text to clipboard". Click that, then paste into a reply. After the extensions is a section named Important Modified Preferences. Since those aren't very relevant to your question, you can delete from there to the end.

Some icons will put themselves where they want and can't be moved.

Thanks, but none of my extensions are nonessential and I have no idea what an unrecognized extension might be.

Yeah, I have a feeling that this is the case. I really hate Google-Do-Evil, but at least the icons in Chrome stay where I put them!

One other possibility besides misbehaved extensions. Occasionally the file that stores toolbar customizations becomes corrupted and fails to update properly at the end of your session (as well as causing many other strange symptoms).

The file isn't easily editable, but you can rename it and customize your toolbars from scratch.

Open your current Firefox settings (AKA Firefox profile) folder using

Help > Troubleshooting Information > "Show Folder" button

Leaving that window open, switch back to Firefox and Exit

Pause while Firefox finishes its cleanup, then rename localstore.rdf to something like localstore.old

Restart Firefox. Hopefully now your preferred icon positions will be remembered.