DC RUM currently does not contain alert which is triggered when Console service goes down. I will add this idea to list of topics to be considered while planning further improvements of product in future releases.
Right now I can suggest you two kinds of workaround which might address your cases:
1. You can consider RUM console as a web application to be monitored by DC RUM, define Software Service and Business Units and define Alert on them
2. In case of loosing contact with Console, CAS displays warning as shown on screenshot below.
Of course I realize that it is not the same thing as an alert, however you might like to use this information for your case.