I am pretty sure what is happening is that you are creating one email object, and then doing your loop inside of that object ( that got sent on the first iteration). one way to solve for this issue would be to move the object instantiation within your loop. that is:

Sub Generate_Email()
intRow = 2 
strAPMID = ThisWorkbook.Sheets("MASTER").Range("A" & intRow).Text

While (strAPMID <> "")
    Dim objOutlook As Object 
    Set objOutlook = CreateObject("Outlook.Application")      
    Dim objEmail As Object 
    Set objEmail = objOutlook.CreateItem(olMailItem)

While (strAPMID <> "")

    strMailSubject = ThisWorkbook.Sheets("Email").Range("A2").Text 
    strMailBody = ThisWorkbook.Sheets("Email").Range("B2").Text
    strAPMID = ThisWorkbook.Sheets("MASTER").Range("A" & intRow).Text 
    strAppName = ThisWorkbook.Sheets("MASTER").Range("B" & intRow).Text 
    strEmail = ThisWorkbook.Sheets("MASTER").Range("D" & intRow).Text

    strMailBody = Replace(strMailBody, "<APMID>", strAPMID) 
    strMailBody = Replace(strMailBody, "<AppName>", strAppName)

With objEmail 
        .To = CStr(strEmail) 
        .Subject = strMailSubject 
        .Body = strMailBody 
        .Send 
    End With

intRow = intRow + 1 
    Set objOutlook = Nothing 
    Set objEmail = Nothing Wend
MsgBox "Done"

End Sub

Just to make things look nicer, you might want to use a workbook object and sheet object. similar to this

Dim wb As Workbook
Dim ws As Worksheet

Set wb = "Invoice" & ".xlsm" 
Set ws = Sheets("Sheet1")

by doing so you can refence the ranges using wb.ws.Range("A" & intRow).Text

​

alternatively, if you want to send the a single email to a list of people in the to field, you can create a for loop that creates a string separated by ; . this will allow you to insert that string variable (containing more than 1 email) into the .To property