This is a potential bug with Live. If you publish reports to Live from datatables with column groups, those reports will publish fine. But if you try to update the report with a table that doesn't have those column groups defined, the reports using those column groups will not render.
The fix here maybe be to undo column group references when reports are published to Live so that when an update occurs with a source that doesn't have those column groupings, the reports don't break.
