Currently there is no logging of user logon attempts*. If there were, it might not prove useful as stated above. Cookies expire in 5184000 seconds. There is a define for this value, 'COOKIE_PESISTENCE' in functions-basic.php
* Actually, you could get a log of sorts by setting the define `DEBUG_LOGIN` to true, also in functions-basic.php. You will get a lot more data than you probably want, though.
The login handling is all done by the script lib-auth.php. This script is designed so that it could be replaced by an equivalent. You could modify it to provide the logging you desire. You would have to be aware of any changes that might be made to the script release to release so that your version did not slip out of date.