You haven’t given enough info to answer definitively, only to guess. Please take the following as editorial guidance for all people posting requests for help, not as a personal attack:
the phrase “after creating a face and modifying it” is very non-specific. There must be millions of ways one could do that. What did you actually do? How did you create a face? How did you modify it? What tools or extensions did you use?
you say “there seem to be breaks in the faces” but don’t point any of them out. What specific problem are you asking for help with?
your picture appears to be in X-ray mode, which doesn’t help to illustrate your point, as one can see through both valid faces and gaps.
your picture doesn’t provide a lot of clarity or context as to what is really going on. Posting a model would be much better.
you refer to “the little black line”, by which you presumably mean the tiny edge at the center of your picture, but “a segment disappeared”…what is a “segment”? Do you mean an edge? A face? Which “segment” disappeared?
With all that said, here are some off-the-cuff suggestions based on typical issues:
Inability to create a face is almost always due to the corner points not being co-planar. This can usually be detected by drawing a diagonal edge. If a triangular face suddenly appears, the other corners are not co-planar with the three you chose.
If you created the drawing using Follow-me or Intersect with, have you tried scaling up first to avoid issues with very small geometry?
Have you tried View->hidden geometry to see where there are hidden edges that might be affecting what you are trying to do?