Internet Explorer 8 Issue

So i'm having the following issue at work with Internet Explorer 8,after i log into the following website http://www.tmhp.com/Pages/Medicaid/Medicaid_home.aspx when i first start explorer in the morning it's fine,window pops up asking me for login and pass,everything normal,but i use 3 different users,but i can't seem to log off unless i close explorer and delete everything: cookies,history,etc

I can't for the life of me figure out how to let explorer log me off normally and let me log in and just prompt me for login and pass like it normally does when i first open it. Any suggestions? I'm tired of this bug. Is it an issue with me or maybe their site? Any way to test this?