When members log in to their account, they have a check-box that says "Remember Me". If checked WordPress will remember the login session for 14 days, only 2 days if unchecked. If they delete their cookies, though, they'll have to log back in next time. Same if they come back from another browser.
I searched and found these two plugins that would allow you to edit those times with ease:
https://wordpress.org/extend/plugins/re ... -controls/https://wordpress.org/extend/plugins/co ... n-timeout/Please let us know if one of them played well with s2Member after you try.