The simplest approach would be to store the Section break type before deleting, then re-apply it afterwards. That way you don't need to concern yourself with what type it was or might have changed to. For example, supposing you wanted to delete Section 2:
Code:
Sub Demo()
Dim ScnBrk As Long, i As Long
i = 2
With ActiveDocument
ScnBrk = .Sections(i - 1).PageSetup.SectionStart
.Sections(i).Range.Delete
.Sections(i).PageSetup.SectionStart = ScnBrk
End With
End Sub
With this code, it really doesn't matter whether the Section break was continuous, next page, first page or even page - it'll be restored to its prior state.