The search engines that come with Firefox / Nightly / etc. are located in the installation directory. The settings for which search engines are hidden / added / etc. is stored in the profile which app update doesn't touch and it sounds like these settings aren't retained for some reason.
Bug 1552664 Comment 3 Edit History
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The search engines that come with Firefox / Nightly / etc. are located in the installation directory and the settings for which search engines are hidden / added / etc. is stored in the profile which app update doesn't touch and it sounds like these settings aren't retained for some reason.