Personálmente por cosas como esta nunca me gustó el BackGroundWorker.

La forma correcta de pausar/reusmir un BackgroundWorker es usando un ManualResetEvent:

EDITO: Fíjate que debes especificar manuálmente los lugares en donde el procedimiento se puede pausar (_busy.WaitOne), y esto debes especificarlo sólamente en el eventhandler DoWork.

Imports System.ComponentModel

Public Class BackgroundWork

    Private _busy As New Threading.ManualResetEvent(True)

    Private WithEvents MyWorker As New BackgroundWorker

    Public Sub StartBackgroundTask()
        MsgBox("Starting the Thread...")
        MyWorker.WorkerSupportsCancellation = True
        MyWorker.WorkerReportsProgress = True
        MyWorker.RunWorkerAsync()
    End Sub

    Private Sub MyWorker_DoWork(ByVal sender As Object, ByVal e As DoWorkEventArgs) _
    Handles MyWorker.DoWork

        For i = 1 To 5
            _busy.WaitOne(Threading.Timeout.Infinite)
            MyWorker.ReportProgress(MsgBox("Thread is working... " & CStr(i)))
        Next i

    End Sub

    Private Sub MyWorker_RunWorkerCompleted(ByVal sender As Object, ByVal e As RunWorkerCompletedEventArgs) _
    Handles MyWorker.RunWorkerCompleted

        MsgBox("Thread Done!")

    End Sub

    Public Sub PauseWorker()

        If MyWorker.IsBusy Then
            _busy.Reset()
            MsgBox("Thread Paused!")
        End If

    End Sub

    Public Sub ContinueWorker()
        _busy.[Set]()
        MsgBox("Thread Resumed!")
    End Sub

End Class

EDITO 2: Un ejemplo mejor elaborado:

' BackgroundWorker Example
'
' // By Elektro H@cker
 
#Region " Usage Examples "
 
'Public Class Form1
 
'    Private MyWorker As New BackgroundWork
 
'    Private Shadows Sub Load() Handles MyBase.Load
'        MyWorker.StartBackgroundTask()
'    End Sub
 
'    Private Sub Button_Pause_Click() Handles Button_Pause.Click
'        MyWorker.Pause()
'    End Sub
 
'    Private Sub Button_Resume_Click() Handles Button_Resume.Click
'        MyWorker.Resume()
'    End Sub
 
'    Private Sub Button_Cancel_Click() Handles Button_Cancel.Click
'        MyWorker.Cancel()
'    End Sub
 
'End Class
 
#End Region
 
#Region " BackgroundWorker "
 
Public Class BackgroundWork
 
    ''' <summary>
    ''' The BackgroundWorker object.
    ''' </summary>
    Private WithEvents MyWorker As New System.ComponentModel.BackgroundWorker
 
    ''' <summary>
    ''' ManualResetEvent object to pause/resume the BackgroundWorker.
    ''' </summary>
    Private _busy As New Threading.ManualResetEvent(True)
 
 
    ''' <summary>
    ''' This will start the BackgroundWorker.
    ''' </summary>
    Public Sub StartBackgroundTask()
 
        MsgBox("Starting the Thread...")
        MyWorker.WorkerSupportsCancellation = True
        MyWorker.WorkerReportsProgress = True
        MyWorker.RunWorkerAsync()
 
    End Sub
 
    ''' <summary>
    ''' This is the work to do on background.
    ''' </summary>
    Private Sub MyWorker_DoWork(ByVal sender As Object, ByVal e As System.ComponentModel.DoWorkEventArgs) _
    Handles MyWorker.DoWork
 
        For i = 1 To 5
 
            If MyWorker.CancellationPending = True Then
                e.Cancel = True
                Exit For
            Else
                _busy.WaitOne(Threading.Timeout.Infinite) ' Indicate that here can be paused the Worker.
                MyWorker.ReportProgress(
                    MsgBox("Thread is working... " & i)
                    )
            End If
 
        Next i
 
    End Sub
 
    ''' <summary>
    ''' This happens when the BackgroundWorker is completed.
    ''' </summary>
    Private Sub MyWorker_RunWorkerCompleted(ByVal sender As Object, ByVal e As System.ComponentModel.RunWorkerCompletedEventArgs) _
    Handles MyWorker.RunWorkerCompleted
 
        If e.Cancelled = True Then
            MsgBox("Thread cancelled")
 
        ElseIf e.Error IsNot Nothing Then
            MsgBox("Thread error")
 
        Else
            MsgBox("Thread Done!")
 
        End If
 
    End Sub
 
    ''' <summary>
    ''' This will pause the BackgroundWorker.
    ''' </summary>
    Public Sub Pause()
 
        If MyWorker.IsBusy Then
            _busy.Reset()
            MsgBox("Thread Paused!")
        End If
 
    End Sub
 
    ''' <summary>
    ''' This will resume the BackgroundWorker.
    ''' </summary>
    Public Sub [Resume]()
        _busy.[Set]()
        MsgBox("Thread Resumed!")
    End Sub
 
    ''' <summary>
    ''' This will cancel the BackgroundWorker.
    ''' </summary>
    Public Sub Cancel()
        _busy.[Set]() ' Resume worker if it is paused.
        MyWorker.CancelAsync() ' Cancel it.
    End Sub
 
End Class
 
#End Region

Entonces, desde el thread principal puedes hacer esto:

Public Class Form1
 
    Private MyWorker As New BackgroundWork
 
    Private Sub Form1_Load(sender As Object, e As EventArgs) Handles MyBase.Load
        MyWorker.StartBackgroundTask()
    End Sub
 
    Private Sub Button_Pause_Click() Handles Button_Pause.Click
        MyWorker.PauseWorker()
    End Sub
 
    Private Sub Button_Resume_Click() Handles Button_Resume.Click
        MyWorker.ContinueWorker()
    End Sub
 
End Class

Saludos