Kenneth Pope has a great site on Responding to Suicidal Risk. The site contains practical advice on risk factors and specific factors to consider with any suicidal client.
The evaluation and response to suicidal risk is a source of extraordinary stress for many therapists. This aspect of our work focuses virtually all of the troublesome issues that run through this book: questions of the therapist's influence, competence, efficacy, fallibility, over- or under-involvement, responsibility, and ability to make life-or-death decisions. Litman's (1965) study of over 200 clinicians soon after their clients had committed suicide found the experience to have had an almost nightmarish quality. Clinicians tended to have intense feelings of grief, loss, and sometimes depression as anyone—professional or nonprofessional—might at the death of someone they cared about. But they also had feelings associated with their professional role as psychotherapist: guilt, inadequacy, self-blame, and fears of being sued, investigated, or vilified in the media. In a similar study, both the short-term and permanent effects of a client's suicide upon the therapist were so intense that Goldstein and Buongiorno (1984) recommended providing support groups for surviving therapists.
As a therapist who has had one long term client suicide during therapy I can certainly say that I experienced all of the above. Avoiding this event is something I can certainly recommend but it is highly likely that many of us will experience this at least once in our professional lifetimes.
Pope provides comments from arrange of professionals on working with suicidal clients.
One of the two main problems in treating suicidal patients is our own anger and defensiveness when confronted by someone who does not respond positively--and perhaps appreciatively--to our therapeutic efforts. It can stir up very primitive and childish feelings in us--we can start to feel vengeful, withholding, and spiteful. The key is to become aware of these potential reactions and not to act them out in our relationship with the patient. The other main problem seems to be more prevalent among beginning therapists. When we are inexperienced, we may be very cowardly regarding the mention of suicide in our initial interviews. We passively wait for the patient to raise the subject and we may unconsciously communicate that the subject is "taboo." If the subject does come up, we avoid using "hot" language such as "murder yourself" or "blow your brains out." Our avoidance of clear and direct communication, our clinging to euphemisms implies to the patient that we are unable to cope with his or her destructive impulses.
What I found most helpful on this site was a section on special considerations. Things to be aware of and to do in these situations. Some of the ideas that stood out for me included:
Screen all clients for suicidal risk during initial contact and remain alert to this issue throughout the therapy. Even clients who are seriously thinking of taking their own life may not present the classic picture of agitated depression or openly grim determination that is stereotypically (and sometimes falsely) portrayed as characteristic of the suicidal individual. In some cases the suicidal client may seem, during initial sessions, calm, composed, and concerned with a seemingly minor presenting problem. Clients who may in fact not be suicidal during initial sessions and who may actually have sought therapy to help them cope with a relatively minor problem may, during the course of therapy, become suicidal. The increase in suicidal risk may be due to external events, such as the loss of a job or a loved one, or to internal events, such as setting aside psychological defenses or discovering traumatic incidents—for example, incest—that had been repressed.