Because your consciousness has not left your original body... its only been copied. The AI or new body may have all your memories up to the point of copy but your original self does not stop.
The idea that you leave your body for a new one is impossible..
Your copied consciousness may live on, but your original one will keep going in your dying body and die with it. All you have done is created a copy..
There is no escaping death.
Right there is no escaping death that has been and is a truism.
But picture if you will being attached to a computer the last, oh lets say 10 years of your life. Besides sharing your thoughts it is a mechanism by witch your being can use the machinery to supplement you life to experience new things and solve problems you could never do unaided.
You (and your brain) die but everything that seemingly is YOU (sans your body and brain) exists on this huge thumb drive.
I dont see that YOU would not be there.
Of course the possibilities didnt exist while most famous philosophers throughout history were pondering the human question.
I dont disagree with your statement you are dead. We wont know what such an existence would be like till such time as the experience has happened (if ever)