Does f secure continue to protect my device if I log out or do I need to remain logged in all the time?
You need to stay logged in to the security client. If you log out, the product looses it's license and expires. This turns off all security features.
There are some differences between operating systems, but for example the Windows version will warn you twice before you can log out.
Once you have installed F-Secure SAFE on your device, the program continues to run at the background, protecting your devices. Login to the portal is only to manage your subscription and to keep track of your protection on all devices. You do not have to stay logged on to the portal.