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After I merge the new added surface with the frames that have been merged, the beam or column or both around the surface disapper. Why does this phenomenon exist? Does it influence the analysis? How to avoid it?

When you merge some entities, and you have 2 coinciding items, in your case 2 edges (the pre-existing edge with a section, and the new edge that in your case is the border of a surface), the resulting merged edge cannot have the property of both edges (of course), so STKO chooses the property of one of the two.

As you have seen in your axample, sometimes it picks the property of the existing edge (which is what you want), and sometimes it picks the other (or nothing if the other does not have a section assined)

In this case you need to re-assign the physical and element property to the new merged edges.