Creating a new line feature, whose length is less than the precision of the dataset, results in a feature without a shape to be added.
When creating new features, the shape is snapped to the precision of the spatial reference of the target layer.
If the distance between vertices in the sketched shape is less than the precision of the target layers' feature class, vertices will collapse and a feature will be created with a null shape.
Contact your database administrator. The precision settings for your data are most likely incorrect.
Please refer to Building a Geodatabase for additional information about precision and setting the spatial reference.