@donandress
Right-click on the input field and choose "inspect". In the DOM view that loads up in developer tools, see if there's "autocomplete=off" on the input element. If so, that could explain why Opera's not saving autofill data for the field. If that's the case, try installing an extension from https://chrome.google.com/webstore/search/autocomplete?_category=extensions that forces autocomplete back on for sites.
If you think something is corrupted with your autofill data, goto the URL opera://about, take note of the "profile" path, close Opera, and delete the "web data" file in the profile folder. You'll lose any autofill data that did save in the past (but not your usernames and passwords) and you'll lose custom search engines you've added, but that might fix things. Just make sure that you then goto the URL opera://settings/addresses and make sure saving and filling is turned on.
You could also try in a test standalone installation to see if things work there. If so, then there's something messed up with your Opera profile or settings or sync or you have an extension that's interfering.
If you think a site is purposely doing this only to Opera, goto the URL opera://flags/#reduce-user-agent, enable the flag, restart Opera, and try things again.
Also, for the problem sites in question, goto the URL opera://settings/siteData, type the site in the search-cookies field, and choose "remove all shown". Then, try the site again.
Also, if you have Opera's adblocker and tracking protection turned on (or an adblocker extension), try with things off just to see if the adblocker is causing the problem. Unlikely, but something you can try.
If you have a specific page that's available to the public and doesn't require an account, you can link to it and we can test.