Hi Larry,
You need to make sure you are using your browser in a way that allows it to save passwords and cookies. Depending on choices you made in the past you might need to reset the browser's settings to allow this. Next time you sign in you can opt to let your browser save your password if it doesn't do so already.
When you authenticate the browser with the verification code delivered to your device make sure to tick the box Remember this browser. It is easily overlooked.
You should find that on subsequent visits your email address and password are entered for you and clicking Sign In will log in without requiring authentication.
You will need to go through the same steps for each browser that you want to use routinely with Apple Support Communities.
tt2