While you may be using the same email for your Xbox and PSN accounts, that isn't automatically the email used for your EA Account as well.
You'll be prompted to log into an EA Account the first time you play any EA game on that platform. If you're seeing repeated prompts to change your password that don't go away when you update your account password, it's likely you have a couple different EA Accounts and you'll need to reset the password for a different, older account instead of the one you've been using.
You can check this by logging in here to see if your PSN and Xbox accounts are appearing linked. If you don't see one or both, that means they're linked to a different EA Account.
If you're unsure of which account that might be or are still running into trouble resetting the password after that, please reach out to an advisor and they can take a look with you.