On Linux the clipboard isn't a place to store data but a way of communication between programs:
If a program copies data to the clipboard it actually doesn't copy anything but just registers itself as the clipboard owner and waits for clipboard-related messages from other programs.
If a program wants to paste data from the clipboard it sends a message to the clipboard owner and requests data in some particular format (like e.g. text). The clipboard owner then answers with data in that format or an error if can't provide data in that format.
After logging out there is no clipboard owner so you can't paste from the clipboard.
There are clipboard managers, e.g. diodon or parcellite, that provide additional features for the clipboard. Maybe you can find one that can preserve the clipboard content between sessions.