I also allow the browser store cookies either in the sittings.

Do you use CCleaner?

Did you check the cookie exceptions?

You can inspect and manage the permissions for the domain in the currently selected tab via these steps:

• Click the "Site Identity Button" (globe/padlock) on the location bar
• Click "More Information" to open "Tools > Page Info" with the Security tab selected
• Go to the Permissions tab (Tools > Page Info > Permissions) to check the permissions for the domain in the currently selected tab

In case you are using "Clear history when Firefox closes":

• do not clear the Cookies
• do not clear the Site Preferences

• Tools > Options > Privacy > Firefox will: "Use custom settings for history": [X] "Clear history when Firefox closes" > Settings
• https://support.mozilla.org/kb/remove-browsing-search-and-download-history

Note that clearing "Site Preferences" clears all exceptions for cookies, images, pop-up windows, software installation, passwords, and other website specific data.

Clearing cookies will remove all specified (selected) cookies including cookies with an allow exception that you would like to keep.

No I don't

I checked the cookie exceptions as you said, information says it allow the website to store cookies but haven't store any password.

You can save passwords on other websites? Have you changed some settings in Firefox?

Yes, no problem except this website. I also report this issue to them but haven't receive any response yet

Can you test it from another computer? A smartphone or something else? You have the same thing?