Impact of student suicide on PhD advisor’s tenure prospects

To get the elephant out of the room first:

If you are contemplating suicide and wondering whether you will hurt the tenure case of your advisor by this, stop this thought right there and get counselling. The tenure case really is of no concern in this question. I am sure your advisor would also agree to this.

Now, assuming that this is a hypothetical question, or it concerns a suicide that already happened.

A suicide of a student will very likely not hurt a tenure case directly. No educated person in her/his right mind would react like "he killed this guy, he must be the worst teacher ever!" I would rather expect a wave of sympathy and compassion about the loss. Of course, whenever a student leaves (for whatever reason), the tenure case is indirectly hurt a little, simply because the advisor needs to start from ground up with a new student, who is likely not going to be very productive for some time.

I'm quite sure that for most professors, their own tenure is about last in the things they care about in this situation. Professors are people too, they care about their students and how they do. In some sense, your students are your children too, as you see them grow up and spend a lot of time together. You're proud if they succeed, and you're sad if they struggle. If a student kills themselves, from the perspective of the adviser it's first and foremost a human tragedy. The impact on the tenure case is really something that's secondary (or tertiary, or even less important).