Generally, the point of a CAPTCHA is to prevent automated use of a service. If we get to the point where CAPTCHA's no longer work in preventing automated access to services, we need to look for atypical use of services.
For example, if a computer passes a CAPTCHA in order to use gmail to automate the sending of spam emails, look for users that mass-spam; typical users won't do that. On the other hand, the computer may try to approximate the usage of a typical user to avoid detection. But if you cant distinguish automated use of your service from typical use of your service, then at that point maybe it doesn't matter so much.
For example, if a computer passes a CAPTCHA in order to use gmail to automate the sending of spam emails, look for users that mass-spam; typical users won't do that. On the other hand, the computer may try to approximate the usage of a typical user to avoid detection. But if you cant distinguish automated use of your service from typical use of your service, then at that point maybe it doesn't matter so much.