Ok. And I assume we are talking about a desktop or laptop and a browser here, and not a phone or tablet using the eBay app?
There was an issue a while ago when eBay changed the login screen and the "keep me signed in' checkbox was not working.
https://community.ebay.com/t5/Getting-Started/Problem-signing-in/qaq-p/28983983Make sure the "keep me signed in on this computer" checkbox in your site prefs is checked and applied per the link above. Also check your browser cookie settings to be sure they are not set to delete cookies.
I have no problems going away for a day or restarting my browsers and not staying signed in. I do have to sign in more often than in the past, especially when listing items, printing labels, messing with site settings, but in general don't get logged out overnight.