From my experience, the web page object should update anytime a parameter value that is used in the URL is updated. One thing that can trip it up is if your parameter is set to show as "Type In" (aka free text), but the parameter properties are set to "List" (instead of "All"). When this is the case, you can free text something into the parameter box and press enter, but it doesn't actually set the parameter value unless the text you entered is on the list in the parameter properties.
If you're still having the issue after double checking your parameter properties, please post a sample workbook.
Hope this helps,