Hmm, what happened?

Many users get a message during an update that Firefox is starting slowly or performing poorly and get a suggestion to restore some default settings. If you click that button, the Refresh feature runs, and your entire settings folder is moved to the desktop inside an Old Firefox Data folder. Do you see anything like that? If so, that would explain it and we can discuss options for setting your search engines back up the way you liked.

If there's no Old Firefox Data folder (or its contents are not recent), is the problem that you can't see any search engines in the search options? That could indicate the program files were damaged during the update or you got an incomplete install. For that I suggest:

Clean Reinstall

We use this name, but it's not about removing your settings, it's about making sure the program files are clean (no inconsistent, corrupted, or alien code files). As described below, this process does not disturb your existing settings. Do NOT uninstall Firefox, that's not needed.

(A) Download a fresh installer for Firefox 40.0.2 from https://www.mozilla.org/firefox/all/ to a convenient location. (Scroll down to your preferred language.)

(B) Exit out of Firefox (if applicable).

(C) Rename the program folder, either:

(64-bit Windows folder names)

C:\Program Files (x86)\Mozilla Firefox

to

C:\Program Files (x86)\OldFirefox

(32-bit Windows folder names)

C:\Program Files\Mozilla Firefox

to

C:\Program Files\OldFirefox

(D) Run the installer you downloaded in #1. It should automatically connect to your existing settings.

Any improvement after this reinstall?

Note: Some plugins may exist only in that OldFirefox folder. If something essential is missing, look in these folders:

• \OldFirefox\Plugins
• \OldFirefox\browser\plugins

A small number of users were managing search engines by hand on disk, editing files in this folder:

C:\Program Files (x86)\Mozilla Firefox\browser\searchplugins

If you were doing that, please see this thread for further background: https://support.mozilla.org/questions/1075655

tyson68 said

The option to change by right clicking search box not available.

Could you try clicking the magnifying glass at the left end of the search box to get to "Change Search Settings" and see whether that helps.