This error may occur after performing one or multiple ArcMap editor undo operations:
"Invalid operation, state delete call is invalid when children states present."
The edit operation is not invalid. The error is because the internal geodatabase structure of the undo/redo stack is not consistent with the current lineage of state operations within ArcSDE. This occurs only after you have done a number of edit operations, then you do a smaller number of undo operations, and finally you attempt to do another edit operation.
Once the error occurs the edit session is corrupt and the only solution is to abort the session by stop editing and not saving.