You can change the build properties of the surface to make a copy of the breaklines. It is located in the definition tab of the surface properties. Look in build and it is the first option.
From help:
Copy Deleted Dependent Objects
Specifies whether a drawing object is copied to the surface definition item if the object is deleted:
Yes: Copies the drawing object data to the surface definition if you delete the drawing object data. When you add a surface boundary, breakline, or point group to a surface, the surface definition stores the Object ID. If the drawing object, such as the original polyline used to define the surface boundary, is deleted from the drawing, the coordinates of the polyline vertices are copied into the surface definition and saved. Thus, the surface boundary definition remains in the surface definition.
No: Deletes the surface boundary, breakline, or point group definition if the drawing object is deleted. The definition item is removed from the surface definition when the surface is rebuilt.
Exclude Elevations
Stacy Dunn