Firefox doesn't have a true "autofill" feature as such. It has a rudimentary form fill feature, that remembers what was entered in the past and offers that data as a suggestion the next time the user is filling out a form in a similar type field.

Suggestions appropriate for standard form fields may or may not be always accurate, as Firefox doesn't recognize all field names in forms; and a lot of forms don't always follow the accepted RFC standards names for web form fields. If you want a real auto fill feature, install an extension which adds that feature to Firefox.
Here's one that has been popular in the past, but the original developer sold it and it has a new commercial owner.
https://addons.mozilla.org/en-US/firefox/addon/autofill-forms/

Other similar extensions:
https://addons.mozilla.org/en-US/firefox/search/?q=form+fill

The website may be using autocomplete=off to prevent Firefox from saving and filling this form data

You can remove autocomplete=off with a bookmarklet to make Firefox save names and passwords and other form data.

• http://kb.mozillazine.org/User_name_and_password_not_remembered

They are all sites which used to autofil. Only new forms and the fields I deleted are no longer saving and inserting the fill data.

How do I "remove autocomplete=off"?

True or not, it used to work. It no longer works for new forms or fields for which I deleted the autofill selection.

I tried both the autofil add-ons. Neither one works.

This has nothing to do with passwords.. I do not wish to remember passwords. It concerns autocomplete which used to work but has suddenly quit working with new forms and with fields on forms which used to work but no longer work since changed.

I don't want "true autofil." I want "rudimentary form fill feature, that remembers what was entered in the past and offers that data as a suggestion the next time the user is filling out a form in a similar type field. " It is no longer working for new forms or for forms which used to work on which I have deleted a remembered entry (it no longer remembers the new entry.)

Make sure that you do not run Firefox in (permanent) Private Browsing mode (Never Remember History).

• https://support.mozilla.org/kb/Private+Browsing

• Tools > Options > Privacy > Firefox will: "Use custom settings for history"
• Deselect: [ ] "Always use private browsing mode"

I have never used private browsing. I do not want private browsing. How do I insure that I am not using private browsing?

You probably aren't using Private Browsing mode, but you can check this here:

• https://addons.mozilla.org/en-US/firefox/themes/solid

You can there also check the setting for remembering form data.

• Tools > Options > Privacy > Firefox will: "Use custom settings for history": "Remember search and form history"
• https://support.mozilla.org/kb/Form+autocomplete

Websites may be using autocomplete=off to prevent Firefox from saving the name and password or other form data.

You can remove autocomplete=off with a bookmarklet to make Firefox store form data.

• http://kb.mozillazine.org/User_name_and_password_not_remembered

Note that Firefox won't auto-fill a saved name automatically when autocomplete=off is used on a form or input field, so you need to double-click this empty field to get a drop-down list.

I don't see how Themes has anything to do with it.

In order to save "Remember search and form history" I had to turn off "remember browsing and download history." But it still doesn't remember my form item.