For anyone who runs into this problem in the future, I ended up reading the file to the end and saving it into a variable. Then converted it back into a memory stream to use for the parser. If an error occurs, I just create a new file with the string. This is the code I used.
Dim id As Integer = (Int32.Parse(context.Request("id")))
'Read full file for error logging
Dim content As String = [String].Empty
Using sr = New StreamReader(uploadedFile.InputStream)
content = sr.ReadToEnd()
End Using
'Convert it back into a stream
Dim byteArray As Byte() = Encoding.UTF8.GetBytes(content)
Dim stream As New MemoryStream(byteArray)
Try
ParseFile(stream, id, content)
context.Response.Write("success")
Catch ex As Exception
Dim filename As String = uploadedFile.FileName
Dim uploadPath = context.Server.MapPath("~/Errors/MyStudentDataFiles/")
'Save full file on error
Using sw As StreamWriter = File.CreateText(uploadPath + id.ToString() + filename)
sw.WriteLine(content)
End Using
context.Response.Write("error")
Throw ex
End Try
Else
context.Response.Write("error")
End If