The idea of a "deep fear of death" is a typical exaggeration and a typical extreme view. Of course, there is no empirical research to support this claim, and it is a bad mistake to try to force one's own world view to fit such a claim. The fact that a single 90-year-old is afraid of death proves nothing - even a healthy 70-year-old thinks about other things than death.
Urban Stoicism always reflects on the orders and sensations of ordinary everyday life. In this case, the feeling that exists in everyday life is the fear of the end of time. But it is a feeling that applies to any practical activity that is considered comfortable, whether it is short-term (say, a party), medium-term (say, a work project) or for the rest of one's life. In all three cases, the bad thinking is that, because the desired activity will eventually end, you will not be involved in organising the duration of the activity, but will 'just keep on pushing'.
The fact that you are involved in organising the end of time means that the end becomes more to your liking. In everyday life, without any drama, you can postpone your own death by eating sensibly and exercising a little. urban stoic can smile with basic good humour even in the face of death! Just as the film Gladiator claims that Marcus Aurelius said: 'Death smiles at us all, all a man can do is smile back'.