OK. In that case, it appears Linksys has fixed the changing UPnP port number issue with the last firmware update (Dec 2014). I have been running Networx for a few days now, and it has continued to work OK monitoring the router, even after sleeping overnight, etc. I'll continue to run this "un-fixed" version of Networx a while longer, just to be sure.
But I still have not gotten an answer from Linksys about why my router did not automatically download and install this update, despite be set to do so, nor why it didn't notice the update even after manually checking for it. I had to download the firmware myself and then install it. They actually asked me if I had an Internet connection!