Feedburner email subscription form 404 errors

I recently added a Feedburner subscribe by email form to a website and have discovered a problem with it. Sometimes the form does not work – the pop-up URL http://feedburner.google.com/fb/a/mailverify just shows a 404 error.

At first I thought that this was just happening in Firefox, which seemed crazy as the browser should not affect things like that.
Eventually, I worked out that the problem was due to being logged in to a Google Apps email account in the browser. Once I log out of the Google Apps account, the form works fine. It also works fine if I am logged into a standard Gmail email account rather than a  Google Apps one.
But if I am logged into a Google Apps email account, submitting the form just leads to a 404 error in all browsers.

I have seen several posts on the Feedburner Google group and other sites about similar problems with the email subscription form.

Logging in to Google Apps admin and turning on the Feedburner service fixes the problem for that domain. But Feedburner is off for Google Apps by default, so that’s not a workaround. It seems that Feedburner isn’t getting much love from Google these days, which is a real shame, as it’s a great concept.