Luminate's permissions are subtractive, not additive. What this means is that if an admin is in multiple admin groups and the permissions conflict, the most restrictive permission wins. So if an admin is in a group with only access to emails and in another group with only access to donations, that admin may end up with access to nothing because the permissions conflict. Generally speaking, we do not recommend that admins be members of multiple admin groups.  A special exception is the CMS admin group, which never conflicts with anything by design. When in doubt, test removing the problem admin from all but one group at a time and see if that sheds light on the problem.

Here is an example for the permission "Donation Form Management":
An administrator is in two admin groups that share this permission. 
One of the groups only has access to View Campaign Reports and the other has access to Manage Donation Campaigns.
This administrator will only be able to report since that is the most restrictive permission. 

Note that this gets more complicated with Multi-Center. If you have a Center A and Center B and each has an admin group that only has permission to see things in the one center, then you can put an admin in both center groups even though the Center A admin group disallows the Center B admins and vice versa.