We detect that and skip sending invites to users when LinkedIn shows a captcha.
It should happen after lots of unaccepted sent invites. It could take some time until you get to that point, but it also depends on the user that it’s sending the invites to.
It’s very important to keep your conversion rate around 30%. The conversion rate gets updated when the application sends followups. If you realize that you get too many responses and you want to stop the invites, disable the invites and keep running the followups so that the conversion rate stays up to date.