Search for and remove cookies matching "thefiringline".
Tools menu -> Internet Options
Browsing History (middle) section, click on "Settings"
Click on "View Files"
Sort by file name by clicking on the "Name" heading in the first column.
Scroll down until you see files starting with "cookie:"
Find cookies where the second column contains "thefiringline.com" or "www.thefiringline.com" and delete all such cookies (select the right lines by ctrl+clicking in the first column, then right click, then pick delete).
Log in again, and see if you still keep getting logged out.
“The egg hatched...” “...the egg hatched... and a hundred baby spiders came out...” (blade runner)
“Who are you?” “A friend. I'm here to prevent you from making a mistake.” “You have no idea what I'm doing here, friend.” “In specific terms, no, but I swore an oath to protect the world...” (continuum)
“It's a goal you won't understand until later. Your job is to make sure he doesn't achieve the goal.” (bsg)