Anybody who upgraded to iOS 6 on the iPhone soon found the random story display on the home page to be broken. It took two days to track the problem to excessively aggressive page caching on the part of Safari.
I finally worked around the problem by varying the URL where the random story is fetched for each request. It’s now working on iPhones with iOS6.
To clear all sites’ data, go to:
Settings -> Safari -> Advanced -> Website Data and clear the data.