Do you mean the search bar on the Navigation Toolbar ?

See:

• Edit > Preferences > Privacy > History: "Remember search and form history"
• https://support.mozilla.org/kb/Form+autocomplete

• https://support.mozilla.org/kb/Search+bar
• https://support.mozilla.com/kb/Location+bar+search

both - search bar and location bar all the settings are ok. checked them many times

Start Firefox in Diagnose Firefox issues using Troubleshoot Mode to check if one of the extensions or if hardware acceleration is causing the problem (switch to the DEFAULT theme: Firefox/Tools > Add-ons > Appearance/Themes).

• Don't make any changes on the Safe mode start window.
• https://support.mozilla.org/kb/Safe+Mode

Try to disable hardware acceleration.

• Edit > Preferences > Advanced > General > Browsing: "Use hardware acceleration when available"

unfortunately, did not help...

Try to reset Firefox.

• https://support.mozilla.org/kb/reset-firefox-easily-fix-most-problems

i am sorry to use your time, and thanks a lot for your patience! but still no... reinstall Firefox? upgrade Ubuntu?...