I do not believe that a firm can continue to be successful if it outsources its core business activities. If it does this, it ceases to have control over the most important aspects of its business. This leads to a situation in which there is really nothing left of the firm and it is very hard for the firm to grow or even to maintain itself.
When a firm outsources, it is attempting to cut costs without harming itself. When a firm outsources its key activities, it is likely to harm itself. For example, let us say that the key business activity for Apple is researching and developing new devices that will appeal to consumers. If Apple outsources this activity, it will no longer be in control. It will be relying on other companies to determine what its next product will be. This is bad for Apple regardless of the outcome. If the outside firm chooses badly, Apple will lose revenue and will see its reputation harmed. If the outside firm chooses well, Apple will become irrelevant.
Thus, outsourcing core business activities is a bad idea. It leads to a situation in which the firm is not in control of its own most important activities.