Unless you just minimise the screen when you want to end your current session on eBay and then open a separate screen to continue any other online activity, you will have to keep on logging in each time you want to access the site, especially if you either close the page using the red box in the corner of the screen with the white cross in it, or if you use the "Log Out" link to close your session down.
Personally I always close the page every single time I've finished using eBay by using the "Log Out" link, as it's safer than just leaving yourself permanently logged on. If somebody else was able to gain access to your computer then all they'd need to do would be to restore the page back to full size from when you'd shrunk the page down after you last used your eBay account and it would be a piece of cake for them to use your account to make unauthorised purchases. Therefore, I would suggest closing the page down properly whenever you finish up with a session on eBay, then when you wish to start another session on eBay just log on by inputting your User ID or e-mail address on the top line, then enter your password in the next line and access the site that way. It's far more secure if you access the site that way, regardless of whether you've recently changed your password or not.
