Some browsers or browser settings are better than others when it comes to this sort of thing.
Try another browser or a private or incognito browser window -- if that works, the problem may be cache or cookie-related.
If you regularly erase your cookies or have your browser set to erase cookies on closure, you will have to sign in and go through verification the next time you go to eBay.
Try using a different link to reach eBay, particularly if you are using an old bookmark that may not be redirecting properly.
Other things that can cause sign-in or verification problems: VPNs, privacy software such as Ghostery or Disconnect, blocking cookies, blocking third party cookies, blocking tracking, some script blockers, blocking JavaScript, some ad blockers -- at least on the sign-in or verification page.
