While there is not an out of the box report for this type of information in the current Jive platform, there are a couple of options moving forward.
1. If you are interested in finding out how other Community Managers have reported on this behavior you might reach out to either the Jive Internal Communities or Jive External Communities groups here in the Jive Works Community
2. If you are seeing an issue specific to the captcha failing in your instance I would recommend submitting a case in your customer group ( MyJive Secret Support Group Administration FAQ ) so that a member of our support team can assist with further investigations into your instance's registration process.
3. If you would like to see this type of feature added to a future release of the Jive Platform, I would suggest submitting an idea to the Ideas for Jive space, where our Product team reviews through top rated ideas when considering new features for future releases.
Thanks, Jesse. I was wondering if there was some clear-cut method, but my next step was to ask the External group.