Is your browser set to erase cookies when you close it? If so, you will be required to sign in again the next time you open your browser and go to eBay, as would using a new device, a new browser or a private or incognito browser window.
There are other things that can cause you to be required to sign in such as using a VPN, hotspot or privacy software that changes your IP-address, or rebooting network equipment that might change your IP-address.
A problem with a blocked or corrupt eBay cookie might cause all sorts of sign-in issues as well.
Try using another browser as a test; if you are able to stay signed in without issues, try manually deleting your eBay cookies once in the original browser, and make sure you browser is not set to block cookies.
