No, your White card does not expire.
However, under National WHS harmonisation measures, the NT WHS legislation was updated in 2011 and the SA WHS legislation in 2012. The legislation in WA has not yet been updated.
In 2016, the unit of competency attached to the White Card was changed to CPCCWHS1001 Prepare to work safely in the construction industry.
If it has been a while since you sat your White Card (i.e. before the unit code change or the WHS legislation change), you may wish to re-sit a White Card course to ensure you have the most current and up to date WHS information. Sometimes, your employer or potential employer, may make it a condition of your employment that you resit.