Q.Peach tree dying branch at a time
What causes a peach tree to die one branch at a time? My Faye Alberta Cling peach tree shows now signs of insect infestation. I have sprayed for peach borers with the best insecticide I can find for it. I have also fed the tree with recommended fertilizer. Two branches died and had to be removed and another branch is showing signs that it will die. The tree has only a few peaches on it this year. I would like to save it because it is difficult to get this type of peach tree.

Peach Trees are know to be affected by numerous insect issues and diseases.
Borers are a likely problem due to the symptoms your tree is presenting along with several other fungal or fruit tree diseases.
The tree is likely partially girdled, thus the slow die back.
Fungicides can be used, but they are not as affective after the tree is all ready showing signs of death.
You are right to remove and dispose of all the infected leaves and limbs.
Here are some links for you that may offer some help.
https://www.gardeningknowhow.com/edible/fruits/peach/peach-tree-borer.htm
https://www.gardeningknowhow.com/edible/fruits/peach/common-peach-diseases.htm
http://www.clemson.edu/extension/hgic/pests/plant_pests/veg_fruit/hgic2209.html