So it is just the update that is not occurring? The update should occur whenever submit the form with the button. It looks like you have the action set to this same page, if you want the form to post to the same page you can just leave the action blank.
If the update is not occurring then the trigger might not be occurring. One way to test things out is to print out the query that is used for the update. To do this on line 36 of the page you posted add a new line and add this in it:
This will let you know if the update is being triggered and what the query is that is being used in the update. Post back and let us know the result of this test.