I've had my eeepc for about 14 months and noticed the same problem.

The same thing also happens to me on my MSI Wind when my thumb strays onto
the touchpad. Fortunately on the Wind there is a Function key that toggles
the touchpad off and on. If there isn't a utility to do the same on the
eeepc someone should write it!

Otherwise one might be able to train the thumbs not to fall on the touchpad
area, but that would not be easy.