If you use Control Panel / User and Passwords and select a local <User Name>, you can manage group membership from the Group Membership tab of Properties. If you select Other and choose a local group, all other group memberships are deleted. If the logon on locally right was granted to one of these groups (and not the new group), the user won't be able to log on.
To avoid this problem, use the Computer Management tool to add users to local groups.
NOTE: You can right click on My Computer and press Manage / Local Users and Groups.