Maybe the psychiatrist saying to not make a big deal of it was intended as, "Don't go wailing around the house wringing your hands and making a loud noise about it." But it always needs to be taken seriously. Even if five minutes later the kid is smiling happily and playing a game with another child, AT THAT MOMENT they felt suicidal.
With my phone callers - I had no chance to tell anyone. And fortunately I wasn't in the position of one of my colleagues, who was on the other end of the phone when someone rang and said, "I've just taken an overdose, I'm not changing my mind, I just didn't want to die alone."
Kids DO feel that bad, but don't always understand the finality of death and choices to die. And when a kid feels that bad, the sense of powerlessness they feel, at that moment, is extreme. Definitely tell the therapist, even if the chid is apparently over it a short time later. It's always worth a mention. For us, we dealt with it at that moment with difficult child 1 but then organised an emergency appointment with the doctor. In our son's case, upping the dose of Zoloft did the trick for him. It was enough to help him work through his feelings without them overwhelming him too much. But I know this is not an option for everybody - it wouldn't work with me, for example. Probably not for difficult child 3 either, since both of us have adverse reactions to antidepressants.
I do agree that it's vital that the child's doctors be quietly informed, preferably quickly. No child should be feeling that bad.
One more point - bringing up the subject of feeling suicidal is NOT going to put the idea into their heads, as a rule. Often the reaction is one of relief, that at last they can talk about feeling that bad. Talking about it is always better than letting them feel alone and bottling it up. If you keep skipping around the topic you may miss a chance to sort out a serious problem before it becomes final. But if you bring up the subject, they may either say, "Yes! I feel that bad! How did you know?" or they could say, "No way! I'd never do that!" and you've hopefully helped them put their pain into a more appropriate perspective. But one thing I'm sure you won't hear - "Hmm, that's a good idea, thanks for suggesting it."
One final rule you can introduce, to someone determined to commit suicide - "Don't leave a mess for someone else to have to clean up." That includes emotional fallout. It also includes a near miss, leaving the subject permanently brain-damaged but aware. You're even worse off but now you can never finish the job. A walk through the outcome for other people can be a short, sharp lesson. But if you think it won't work - don't go there.
My suggestions are definitely not intended to replace expert intervention. They're only something to pull out when you can't get the help you need right then.
Marg