By design, PalmOS disables all drivers and background apps when you perform a warm reset (pinhole + ArrowUp). This allows you to still use the device if you accidentally install troublesome or incompatible software.
If TealLock is already locked prior to the warm reset, then the handheld will come up with the standard Security lock screen after booting up, continuing to secure the handheld until your system password is entered. This will also occur if you have any apps marked as 'protected' in TealLock in order to keep someone from trying to circumvent app-protection with a warm reset.
If the handheld is already unlocked when you warm reset, however, and no 'protected' apps are specified, then the handheld will continue to be unlocked after the warm reset, and TealLock will not be able to automatically lock because PalmOS is running in safe mode and not processing background notifications.
You can optionally force a system lock even on a warm reset by adding at least one app to your 'protected' apps list. This will keep PalmOS in a semi-locked state at all times, which is normally not a problem. In a few cases, however, it may confuse a few apps (like BackupBuddy) that are written to not do background activation when they think the system is locked.