Hi William,
LinkedIn limits the number of requests that they permit against their API, and they are constantly changing/reducing it. Our Profile page uses two ways to try to query LinkedIn to minimize the impact of their limitations. The first is a third-party tool, FullContact, which is the source of the message you are seeing. The second is a personal LinkedIn account, which you can set up under Settings > ClickDimensions Settings > Connectors. You can add anyone's LinkedIn username and password there - they don't need any special permissions nor a paid LinkedIn account, just as long as they can sign into LinkedIn. If you set that up, we will also use that account to query the LinkedIn API.
Even with these two options, the LinkedIn API is very inconsistent, as it does not always return the same results you would see if you simply logged into LinkedIn and did a manual search for someone, so you may still see the message you were getting.