Are you using a VPN? Or privacy add-ons such as Ghostery or Disconnect? If so, try disabling those.
Set your browser not to erase your eBay cookies, and do not change your IP address between sessions, and in most cases you should not need to go through verification unless eBay detects a problem with your account.
Some browsers, or browser settings, may be better than others when it comes to avoiding the need for additional verification.
If eBay notices something suspicious -- like simultaneous sign-in attempts from far flung locations -- eBay may require additional verification as a protection measure to prevent your account from being hijacked.
