If you have this problem, than you have the 'Glidepoint touchpad' selected. There are two 'mode' buttons at the top, 'Glidepoint touchpad' and 'Precision Touchpad'. Select the 'touch pad' tab and select the link for 'click to change the touchpad settings'. This brings up the Mouse properties window. To fix this frustration, click on additional mouse options at the very bottom of the page. In fact, you can use the mouse tapping to turn that setting on and back off (hint, if it is off, than you shouldn't be able to tap it back on, but you can). If you have the Glidepoint driver, than you will be very frustrated that the 'Settings/Devices/Mouse and touchpad/Allow taps on touchpad' is completely ignored.
If you have an Alps glidepoint touchpad as on a zBook or many other computers, these instructions are completely wrong as the entire menu system has changed.