Hmm, that shouldn't happen. The two ways to change the default search engine on the search bar drop-panel are:

• right-click the search engine icon and choose Set as Default Search Engine from the short context menu
• hold down the Ctrl key as you down-arrow through the search site icons (Ctrl is on Windows, not sure about Linux)

If you are left clicking or arrowing down without holding Ctrl, your default should not change.

Are you using an add-on to modify the search bar?

I figured it out when you mentioned CTRL. I've been accessing the search bar with the keyboard shortcut (CTRL-N) and keeping my finger on CTRL while arrowing through my search engines.

Thank you.