Step 1: Install sqlite3. (Look for "Precompiled Binaries for <your operating system>") https://www.sqlite.org/download.html

Step 2: Find your profile. https://support.mozilla.org/en-US/kb/profiles-where-firefox-stores-user-data

Step 3: Open terminal on OS X or command prompt on Windows and cd or dir to your Firefox profile.

Step 4: Type "sqlite3 places.sqlite". You should see "sqlite>". If this doesn't work then you haven't found your profile or you haven't installed sqlite3. (Although, it's possible these instructions don't quite work on Windows. I haven't tested on Windows.)

Step 5: Type

delete from moz_hosts where host like 'example.com';

(But replace example.com with the website that Firefox keeps suggesting.)

Firefox should stop suggesting example.com

It might be slightly easier to use the SQLite Manager extension:

https://addons.mozilla.org/firefox/addon/sqlite-manager/

Adding some screen shots. SQLite Manager adds itself to the classic Tools menu. If you do not normally display the menu bar, on Windows, you can tap the Alt key to display it temporarily.

Please note that it's not a good idea to delete directly from other tables in the Places database because there are various interdependencies among them.