When I use the Mirror modifier and move vertices away from the "mirror," the top "face" splits, making a large hole between the faces. Filling the hole voluntarily is quite annoying.
Mirrored...
Faces Split.
Is there any way to fix this problem? I don't see it happening with any other user on BSE.
Note that the two later-mentioned options are not checked because this photo is a cropped version of one that came from the Blender Reference Manual.
You need the Merge option. Clipping, too, would help.
The Merge option will join two vertices (1 real and 1 generated by the Mirror modifier) into one. The two to be joined are specified by each being within the Merge Limit: of each other. 0.001 is a good default value, so I would leave it there.
This prevents real vertices from breaking the "mirror." This will make joining the vertices a lot easier because you can just grab the top 8 faces (in your case), key G, then Y, then slide your mouse left to bring the sides together and LMB to confirm when the vertices stop moving as they hit the "mirror." The bolded part shows how Clipping factors into merging the vertices.
Do keep in mind that once you enable this and merge the vertices, you will not be able to move them away from the mirror for the following reasons.
Think of it like constraints. A "merge" constraint merges the vertices into one; they can no longer be separated.
A "clipping" constraint (for some reason) still treats the vertices as two. Moving either away from the mirror would pull its partner through. That can never happen.
If you want to move a joined vertex away, turn off Clipping.
