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After a group content type is created, changing the machine name and then re-saving the content type will cause the checkboxes on the OG Node - Group Permissions page to disappear. A message is set and displayed on the next page load that contains multiple errors like this one:
Warning: Invalid argument supplied for foreach() in element_children() (line 6282 of /og-sandbox/htdocs/includes/common.inc).
Changing the machine name back to the original name will fix the problem.