With Steam Guard, Steam saves a cookie to remember your computer or browser.
If you are being repeatedly asked for a Steam Guard code on the same computer, you will need to ensure your browser has cookies enabled.
Additionally, please note that any of the following browser settings may keep your Steam Guard cookie and login credentials from staying stored for your next login:
Your browser must have cookies enabled for Steam Guard to work properly.
Please follow the instructions below to enable cookies and turn off other browser features that may be interfering with Steam Guard:
Running programs including security software that clear internet history, delete other unused files, or that clean up orphaned registry entries may have a setting to clear cookies as well. Disabling this feature will prevent this issue from occurring when logging into Steam via your web browser.