I spoke too soon. I tried recording the macro differently. The problem wasn't in the Consolidate code, it was because I was trying to import the subproject to the same row each time. I tried the following and although I need to tweak it because it leaves empty spaces between the subprojects, it still imports them all.
Sub InsertSubProjects()
'Declare the variables
Dim projPath As String
Dim projFile As String
Dim r As Long
'Specify the path to the folder
projPath = "C:\Users\isaacc\Documents\Schedules\Open_Jobs\"
'Get the first file from the folder
projFile = Dir(projPath & "*.mpp", vbNormal)
r = 1
Do While Len(projFile) > 0
'MsgBox projFile
SelectTaskField Row:=r, Column:="Name"
ConsolidateProjects Filenames:=projFile, NewWindow:=False, HideSubtasks:=True
'Get the next file from the folder
projFile = Dir
r = r + 1
Loop
End Sub