What causes an HTTP 405 "invalid method (HTTP verb)" error when POSTing a form to PHP on IIS?

I have one form in a PHP (5.2.9-1) application that causes IIS (Microsoft-IIS/6.0) to throw the following error when POSTed:

The page you are looking for cannot be displayed because an invalid method (HTTP verb) was used to attempt access.

It's an HTTP 405 status code. All other forms in the application work, so I believe that the IIS 'verbs' setting for PHP pages is correct.

This is a customer's server, which I have no access to for verifying settings or testing code. All I can do is send the customer replacement files. Other customers on IIS servers have no such issue.

The form is perfectly straightforward:

<form method="post" action="index.php">
    ... fields ... 
</form>

What can cause IIS to throw that error on one form only, but work fine on others?