Mitch “Snapshot” Milam to the rescue once again:

There may be a time, when working in the Dynamics CRM form editor, that you notice that the form editor will not allow you to move a field from one section to another. Have you ever seen that?

It is not a problem with the form editor, it is a problem with the field.

Although it may not be clearly visible, some fields are actually configured to take up two columns, by default. If your destination section is only one column, then the form editor will not allow you to move the field into that section.

The solution is simple: Edit the properties for the field and change the formatting to one column (or whatever you need to, to match the section you are moving into).