The /var/log/messages file really should have someting relating to shutdowns in it, for instance mine (CentOS 5) has lines like this:
Jul 18 23:00:13 nero shutdown: shutting down for system halt
Jul 18 23:00:27 nero kernel: Kernel logging (proc) stopped.
Jul 18 23:00:27 nero kernel: Kernel log daemon terminating.
Check your /etc/syslog.conf or /etc/rsyslog.conf or equivalent to make sure logs are going there. You'll probably need root privileges to read the log files.
Also, while it's not shutdowns per se, the "last" command should report reboots.
Is there really nothing at all in the logs around the time you last shut down?
For your testing, bear in mind that your computer only knows it has 10 minutes left because of the information the battery is reporting, which may or may not be accurate. Rather than waiting for shutdowns you could look at the ACPI information directly. On my laptop it's here:
Under there, the "state" and "info" files look interesting. You could watch the remaining capacity in the state file while you're running your laptop under various conditions to see how quickly it drops.