I don't think the RAIM prediction is that smart that it will look in to the future and predict that a satellite will develop a fault while you are enroute.
So even if there isn't a legal requirement for it, I think "It's good airmanship" should apply.
The RAIM prediction in the box comes from an almanac - it won't detect the failure of a satellite that occurs after that almanac is published.
From memory the almanac in the box is downloaded once a week, at least on the type I fly.
While the RAIM prediction data from Airservices might be a couple of hours old, the data on your GPS/FMS is more likely several days old.
A RAIM prediction is totally different to a warning or failure.