I have a profile that needs to allow an administrator access to their log in, but by going to My Settings -> Personal -> Grant login access they get an insufficient privileges error.
What permissions do they need to access this? 'Manage Login Access Policies' is checked for the profile
With Summer 15, admins with “Modify All Data” delegated admins with “View Setup and Configuration” can login as any user without the user granting access. This should be auto-enabled. If you have restrictions you may need to contact salesforce to enable the ability to login as.
BUT, for some support orgs, if the admin restricted access, or if the user has a license or a package associated with their username that restricts access, admins cannot login as them, check security controls - Login access policies.