A BizTalk map only operates on the message data, not the message context.
However, if you perform the map in the receive port then the only the message data is modified, while the message context remains intact. ( with the exception that properties are promoted from the output message based on it schema and these properties may overwrite existing properties)
If you perform the map in an orchestration you create a new message, with a blank context, so you must copy these properties yourself e.g.
In an message assignment shape in the construct message shape after the transform:
OutputMessage(Mynamespace.MyProperty) = InputMessage(Mynamespace.MyProperty);
or to copy all properties:
OutputMessage(*) = InputMessage(*);