I only see such messages after erasing my browser cookies, changing my IP-address, using a brand new browser, or signing in to an unfamiliar eBay site such as ebay.fr instead of ebay.com.
Using a VPN or hotspot, or using certain kinds of privacy software can change your IP-address, which would cause you to go through verification again the next time you signed in, and would generate such a message.
If your browser is set to erase cookies when you close it, or if you are using a cleaner program to periodically erase your cookies, then the next time you sign in you will have to go through verification again.
There may be other things that can cause additional verification, such as if your account has sign ins from far off locations that might cause eBay to use heightened security features.
A corrupt or blocked browser cookie can also cause issues; it might be worth manually erasing just your eBay cookies once to see if that makes any difference, if none of the other situations apply.
