What makes you say "clicking it has no effect"? Is it that you don't see an email in then inbox of your invitee? If so, then I think you just need to wait for a while. It seems to me that mail delivery delay is a big problem for Apple when any invitations, password reset, ownership verification, or similar activity ever needs to be done.
You probbably don't like that answer. I sure don't, so I'll give you some guidance on how to look into what *IS* actually happening when you press the button - simply Chrome / Firefox Developer Tools. Both of those browsers have them as a standard feature in the browser, so you don't have to install any plugins or extensions. If I remember correctly, I don't think M$ added anything comprable until IE 10 - I'm pretty sure IE 8 won't have the Developer Tools feature.
Debug the Button Yourself
Start up either Chrome or Firefox.
Visit the page with the button you are interested in proving that it *IS* or *IS NOT* doing anything - right click on it, then select "Inspect Element".