Christopher made a bunch of changes to his community and now hardly any members are joining. He's dropped from 5 members joining per day to 1 (on a good day).
How do you diagnose what happened? You look at the following metrics:
1) Are less people visiting your site?
Multiply users by % new visits. If this number is in decline, it could be a change that altered the search ranking or killed inbound links. Compare where the traffic is coming from before and after. Is it a drop in organic search, direct visits, or another source? It's usually a decline in search rankings.
2) Are people clicking on the option to register?
Track the unique visitors to the registration page of the community. Is it up or down? If down, it's that people simply aren't finding the place to register anymore. Make this more visible on the page (or use a clear prompt to join).
3) Are they completing the registration form?
Track your own database here or visits to the post-registration page (make sure you have one). If it's down, it's probably a case of reducing the information the form asks for.
4) Are they opening the confirmation e-mail?
This might be harder to track, you can try using an autoresponder tool like aweber (not perfect) or including an image that is brought from the site. If it's down, it's probably that the from: line or the subject line causes it to either end up in the spam filter or they're simply deciding not to open it. It might be that the confirmation e-mail takes too long to arrive.
5) Are they clicking on the link to register?
Now use your analytics to check they are actually clicking on the link to register. Your database can also show you this.
At some point, something down this line broke. In this case it was the SEO rankings caused by rewriting content on the site.