Although the period of time that a peach stays fresh does vary depending on a few different factors, typically they stay good for at least a few days if they are properly refrigerated.
Usually peaches will stay good for up to a week if they are in the right part of a fridge, though that is not always the case. If peaches are left outside of the refrigerator such as on a kitchen counter top, they usually go bad within one day of being left out.
Because peaches can be sensitive to non-refrigerated climates, it is important to put them n your fridge as soon as you get home.