Well, you can't keep the map active if you are not connected because the thing most basic to it's accuracy is the fact that it constantly updates and will refresh whether or not you have a connection.
Perhaps you could take screen-grabs at regular intervals and paste them into a field for display if network loss occurs. Or you could do a saveAs PDF and have a button for accessing the PDF.
What I don't understand... as I am not familiar with that custom function... what the advantage of using a container field is... when the web viewer would normally used for this purpose? With the web viewer I know you can monitor the contents and check for keywords which when they aren't present accesses the alternative image.