It would appear that Apple have changed the way homescreen/standalone web apps work in iOS 6. According to various blog posts (example) these apps now get their own dedicated s
You can connect your device and open Safari's web inspector on your computer and run document.location.reload()
in the console tab to reload the page.
Before reloading you can press Option+Command+E to make sure the cache is cleared.
Instead of above you can also press Shift+Command+R to reload the page without cache but sometimes it hasn't worked for me.