Websites that are secured with HTTPS will not pass referral information to invalid/insecure sites (HTTP). So if your website is secure but other partner websites are not, the referred data is not being passed. Visits are still being recorded, but because the referred data is not passing, you are unable to tell where exactly the visits are coming from.
To fix this issue, the originating site (with the links to other sites) need to use the meta referrer tag, OR the second site (that is being linked to) has to be secure and the links pointing to that site need to also be secured.
So, the root of the issue is secured sites to non-secure sites. Non-secure sites to other non-secure sites do not cause the issue, nor will secure to secure sites.
It's also important to note that the latest specification for meta tag is not supported in every browser.
To learn more about securing your website, read this blog post explaining the importance of converting your website to HTTPS.