If your browser is not set to clear your cookies, and you are not using a VPN or a hotspot, or privacy software that hides your location, or using certain kinds of security settings to block third-party cookies or block tracking then you may have a problem with a corrupt eBay cookie.
If you are blocking third party cookies or blocking tracking, try disabling that feature on the eBay sign-in page and the Captcha page as well.
Do you encounter the same thing if you use a different browser to sign in more than once? If not, try manually deleting just your eBay cookies -- clearing all cookies may not work if one cookie is blocked or corrupt, but manually erasing eBay cookies one by one should work.
If that does not help, then perhaps eBay has noticed something about sign-ins to your account that are suspicious, such as multiple simultaneous sign-ins from disparate locations. If you are not doing that, perhaps someone else is, or someone else is trying to do that.
