Recently a customer reported that on some team sites that the “Add new user” link had disappeared off the Site Users web part.
Assumptions were initially that the permissions had somehow changed. This was quickly ruled out.
The problem arose when the number of people in the Site Users (and by implication, the site members group) got to 99 or higher. When that happened the “Add new user” link would disappear.
The fix was to increase the number of items to display in the site users web part up to a number where the behaviour would not be seen.
We increased the number to 1000 and the problem was resolved.
The follow on action was to write a PowerShell script to loop through all the sites and modify the web part property and update the site template so new sites used the same settings. I’ll follow up with another post on that process another time.
Hope this helps you.