Strong password offered by Safari not saved in Keychain

I found one answer that worked for me that I only saw suggested one place for the past few hours I've been trying to figure this out: Sometimes the issue has been that I evidently had once logged into some websites and accidentally clicked the "Never remember passwords for this site" option. I had done this probably before I felt comfortable with the idea of using keychain. The solution in this case, and perhaps others, is to go into keychain, delete the current entry completely, then go to that website and change the password. It then gave the pop-up box with the option to save the suggested password in keychain. That worked for me on several websites where it refused to save the "Strong Password" it had suggested. I'm sure there are still some websites that just won't allow suggested passwords, in which case you can go to the "Keychain Access" App on the Mac (spotlight search) and have it generate a suggested password there (or just make your own complex password) and manually update the website's password. In order to keep from having to use the "forgot password" option, the thing to is not accept the "Strong Password" if it doesn't ask to save it in iCloud. Then do what I suggested above about using "Keychain Access" before saving the new password. Hope this helps somebody. It is so frustrating spending the whole night figuring something like this out.

Hello snusmu,

Thanks for visiting Apple Support Communities. We understand that when using the option to choose a created strong password, it doesn't always save to the keychain. To be sure we're on the same page, are you using iCloud Keychain? More information about iCloud Keychain can be found here, just in case: Set up iCloud Keychain

Complete the following steps, testing after each one to see if it resolves the issue:

• Be sure you're fully updated. The description shows you have macOS Big Sur 11.1 installed. The current macOS version is 11.2.1. Update the software to see if that helps: How to update the software on your Mac
• Delete the password entry, then save it again: How to find saved passwords on your Mac
• Make sure you're not using a private browser as the password won't save: Use Private Browsing in Safari on Mac

Let us know how it goes.

Take care.

Also, I've noticed a few times that it doesn't ask to save the password until I log out of the website.