Typically I only see such not-a-robot or Captcha verification screens immediately after erasing my browser cookies and signing in to eBay once again.
If your browser is set to erase cookies after each session, or you are using a cleaner program that erases your cookies on a set schedule, this can result in needing to go through Captcha verification after that happens.
Are you using a VPN or a hotspot? Privacy software like Ghostery or Disconnect?
Any of those can potentially cause verification issues.
If none of those things apply, your browser may be having issues saving or updating your eBay cookies. Blocking all cookies, blocking third party cookies, blocking scripts or using enhanced tracking protection might cause such issues. Try changing your settings or try another browser without those settings to see if you avoid Captcha issues that way.
If another browser works better, try manually erasing just your eBay cookies in the original browser once; that might help if the problem was with a blocked or corrupt cookie, but if you are having problems with multiple browsers or devices the issue may be with your particular settings or your network.
