I needed to add an error handler for the FileSystemWatcher
fileSystemWatcher.Error += new ErrorEventHandler(OnError);
And then add this code:
private void OnError(object source, ErrorEventArgs e)
{
    if (e.GetException().GetType() == typeof(InternalBufferOverflowException))
    {
        txtResults.Text += "Error: File System Watcher internal buffer overflow at " + DateTime.Now + "\r\n";
    }
    else
    {
        txtResults.Text += "Error: Watched directory not accessible at " + DateTime.Now + "\r\n";
    }
    NotAccessibleError(fileSystemWatcher ,e);
}
Here is how I reset the SystemFileWatcher object:
   static void NotAccessibleError(FileSystemWatcher source, ErrorEventArgs e)
    {
        source.EnableRaisingEvents = false;
        int iMaxAttempts = 120;
        int iTimeOut = 30000;
        int i = 0;
        while (source.EnableRaisingEvents == false && i < iMaxAttempts)
        {
            i += 1;
            try
            {
                source.EnableRaisingEvents = true;
            }
            catch
            {
                source.EnableRaisingEvents = false;
                System.Threading.Thread.Sleep(iTimeOut);
            }
        }
    }
I think this code should do what I want it to do.