Fear is a probable cause of death because there are different categories of fear . Fear can be very serious at times because it is one of the very strong emotions that can be triggered mostly anywhere in the body system, the emotion 'fear' is used a lot of times in stance of explaining extreme cases that cause fright. So if too much adrenaline floods the heart it can cause cardiac arrest or heart attack. This explains how fear can cause death scientifically.
Perhaps it is possible for people to die of "fear". Intense terror can obviously have a tremendous negative affect on the body, possibly enough to kill a human being. However, when you ask, "Is fear THE cause of death", you are asking if it is the ONLY one. Of course, it is not. Disease, old age, accidents, etc. Are causes of death. There are many, and I'm sure "fear" is not the most common.
Fear cannot be t h e cause of death, since other things can cause death as well. Besides from that semantic nagging (sorry), I'd say quite the contrary, since the only reason fear exists is to prevent death. Considering a world without fear, all living and half-way conscient beings would immediately go extinct.
For example, what causes us not to consume poisonous substances? Fear of death. Even if dangerous situations were still painful, we could consider touching a hot stove. Being painful I'd maybe draw my hand away once I touched it, but without fear there'd be no reason to not touch it again a moment later. And again and again...
So no, I don't think that the few deaths which are caused by heart attacks (etc.) compare to the countless deaths fear has prevented over billions of years.
I've used the saying 'scared to death' a few times in my life but I'm still here...
A strange question and one easily answered I think. Fear, as stated in the title, is not an affliction such as sickness nor is it a result of an instance such as being hit by a bus. Fear is a by-product, conjured by the human psyche over millions of years to protect itself from dangerous situations. Argument's could be made that rock climber could suddenly become scared and lose his footing resulting in a plummet to his death but this is not fear-induced death, this is an example of the human propensity to remind us to not be clinging to the side of a sheer incline and a bad grip.
The cause of death is sickness, old age, serious injury, heartbreak. Fear is a choice that you make, you choose that you want to be scared of something. Fear could be totally eliminated in the world. We fear things, but most of the time, it's not that thing that kills us.