Why does the audit log show that everytime I log on, I log off immediately afterwards?

This is a reflection of the implementation of the security checking. Each time you perform an action in the Platform Management Console (like logging on or starting/stopping a service), the Platform Managmenet Console checks your credentials. It then immediately issues a call to "log off" or end the credential checking until another action is performed.

If your audit log is filling up too quickly, rename or purge the file regularly.