Wow! Thanks for all the responses everyone. It seems that many of you think Ts do not like working with suicidal clients, but there are some of you who feel very strongly about the way a T responds to such a client - that it's not about whether they like it, but how competent they are at handling the situation.

Some of the reasons Ts don't like working with this client group I see recurring in the posts here are:

-liability if client does commit sui
-stress of caring for someone whose life is in the balance
-lack of confidence or competency in working with this group