When the news is the primary cause of the ongoing tragedy . . .

is it morally responsible for it to keep behaving the in the same fashion?

At this point, there's no doubt about it. The news is feeding a certain violent event.  Indeed, the attention of the news medial on it feeds into the psyche of those who commit it, causing it to repeat.

Now, by no means, can we suggest that the media is the sole cause nor is it the existential cause.  But it is the immediate cause. 

This is interesting, at least in the abstract, in that this occurs in an atmosphere in which its repeatedly suggested that the Second Amendment to the United States needs to be very much curtailed or perhaps even eliminated in the name of public safety.  But everything that could be said in that fashion can equally be said about the First Amendment.  Indeed, those who view the Second Amendment as inherently weak in these regards should, if they are honest, concede that this is even more the case about the First. 

The reason we don't have this discussion, however, is because people are so focused on the First Amendment being necessary for a free state, it can't be restricted in any fashion.  We are, therefore, not willing to tolerate any restrictions upon it of any kind whatsoever.  The last battles of this came in the 1980s when an effort was made to address pornography and that got nowhere.   Indeed, things have gone in the opposite direction. That being the case, there's going to be no effort to restrict news broadcasts and the like that are causing the repeated event.  And maybe there shouldn't be.  But if restricting an immediate an obvious cause is beyond the pale, then restricting a less immediate one should be as well.

None of which means that the news media, which likely knows in the back of its mind, but only in the back where it's cherished view of itself covers it up, that it is causing this to occur can't self restrict.  It'd be unusual in the extreme, but by  the same token in recent years the New York Times has taken the position that once undecided issue will be treated as decided in its pages.  The news media could self blackout.  But maybe it shouldn't.  It won't, however, as it can't imagine itself acting that way in modern times, even though it very much did at one time.