Safari does retain "Remember this browser" data, and websites have to send a login code repeatedly

I am aware of what is expected and what is occurring. We are not denying your issue.

It could be just a Safari bug or it could an issue with your specific computer setup (third party apps & settings), but you have not tried it with any other browsers to confirm. If you clear out the browser cookies, or those cookies don't get saved, then you will have this problem. You need to do the proper troubleshooting before you can even begin to blame Safari.

In fact, clearing out the browser cookies for that website may even help if those cookies have become corrupt. Of course clearing out the cookies will cause all customized settings for that site to be reset to defaults.

Clear cookies in Safari on Mac - Apple Support

Booting into Safe Mode is another test.

Creating a new macOS user account & logging out of your main user account, then logging into the new user account to test Safari is yet another test to localize the problem.

All of these tests will provide more data into the issue & its scope which may provide us with a way to help you assuming the website itself is not broken in some way.

Your thread has been viewed at least 70 times and no one else has chimed in as "Me Too" or provided any other options. Seems pretty clear you need to do some troubleshooting and/or use another browser (assuming the other browser doesn't have the same issue).

If you don't want to do the work or refuse to use another browser (even for testing), then that is your choice. That leaves only one option for you......live with the issue and provide Apple with product feedback here and hope others are also having that same issue & reporting it and hoping Apple will fix it (you may be waiting a long time):

Feedback - macOS - Apple

Chris_Lira wrote:

All good points- thank you. I have been wondering if I have some setting on Safari that is contributing or causing. I poked around a bit and didn't see anything obvious. I will try selectively deleting some cookies. I was also wondering this: like most people, I have 3rd party cookies blocked. So mybank.com should be able to set cookies for mybank.com, but can it set cookies for authenticate.mybank.com, or identity.mybank.com? I would think so, but I need to add that the list of things to look at.

Cookies are usually by domain, but a site can divide its cookies up into other sections as well. I know with Apple.com there are about 3 different sections for me (maybe even 4 or 5). It can be hard to tell which cookies go with a particular part of the website (usually I end up deleting a cookie for the wrong part of the site).

Also, look at any browser extensions.

One would think it would be a first party cookie, but it all depends on how the website has implemented things. A quick check would be to allow third party cookies (or test with a different macOS user account by blocking & allowing 3rd party cookies to see if it makes a difference).

AFAICT, this has nothing to do with Safari, it is just how these sites work. That is two-factor authentication working.

But in case I'm wrong, you can try using a different browser, like Firefox (please avoid the gluton and data syphoning Chrome...), and see if it behaves differently.

Chris_Lira wrote:

I HATE 2-factor authentication for exactly the reason I cited- the impermanence of phone numbers(not to mentioned SIM stealing), and do not have it turned on at any sites. Aside from that, what would be the point of "Remember this browser" if not to bypass this additional step away?

I find it odd that comment about "impermanence" of phone numbers, but maybe that is dependent on where you live. Ever since I got my first mobile phone, well over two decades ago, I have kept the same number - across multiple dumb and smart phones, and also multiple providers. Phone number portability is assumed where I live (Portugal, and I believe the rest of Europe as well), and providers are mandated by law to allow it.

I don't want to use another browser, as I like the syncing of bookmarks, etc., across sites that use using Safari with iCloud provides. I'd rather understand why it's not working on Safari.

For security (to keep you safe from hackers) financial and others institutions are using 2 factor authentication and there is nothing that you can do to change that.

Chris_Lira wrote:

I HATE 2-factor authentication for exactly the reason I cited- the impermanence of phone numbers(not to mentioned SIM stealing), and do not have it turned on at any sites. Aside from that, what would be the point of "Remember this browser" if not to bypass this additional step away?

Unfortunately all the miscreants out there have forced us into this new way of life. We are all being punished for all the scammers out there.

I don't want to use another browser, as I like the syncing of bookmarks, etc., across sites that use using Safari with iCloud provides. I'd rather understand why it's not working on Safari.

Keep in mind this is a test as well as a possible option if successful. If another browser behaves the same way, then it means that is just how that website is operating. Or perhaps you have some third party software installed which is interfering with the normal operation of macOS and/or Safari.