Thanks for your inquiry. ~ We appreciate your patience :-)
The default timeout is based on browser session. A login cookie will last for a single browser session. So closing all tabs and your browser down completely will log you out. That ends a browser session. The default behavior also sets a maximum of 2 days on a single session. If you should NOT close your browser down for 2 days, you will still be logged-out automatically, because of this maximum time limit.
If the “Remember Me” box is checked during login, you will stay logged in for 14 days. Even if you close your browser and come back later, you are still logged in.
It is also possible to change the expiration times if you like. This requires a small MU plugin.
Please create this directory and file:
/wp-content/mu-plugins/s2-hacks.php
(NOTE: these are MUST USE plugins, see: http://codex.wordpress.org/Must_Use_Plugins)
(See also: http://www.s2member.com/kb/hacking-s2member/)