How does the MAC warranty work?

How can I get my defective Mac-Mini replaced?

Purchased August 2014.

Executive Support acknowledges that it is defective. Apple engineers cannot find the problem. However, Apple refuses to replace it. Rather, I must work with Executive Office Reps. until the "root cause" is found.

From the time of purchase, more than ten months ago, this computer has had various problems:

Slow; Frequent freezes; many error messages; continuous popups . . . making it difficult to run my business.

August through January 2014, I took it to to the Apple Store and Phone Support dozen+ times. Many temporary fixes including complete software reinstall and hardware diagnosis 2x. Every time, these temporary fixes deteriorate into the same problems.

I got in touch with the Apple Executive Office in February 2015, and have spent hundreds of hours working with them to find the "root cause"

They say my only option is to continue working with them until the root cause is found. The warranty expires in about 40 days, but they will extend it since the problem started before (11 months before) I asked for support. As I understand it, I have no recourse but to continue spending hundreds of Apple hours and my time. I can go no higher than the Executive Offices.

As a long-time Apple advocate, I would not believe the above information if I were not personally experiencing it. The time, stress, and lost business this problem continues to cause me is enormous. I began keeping detailed records in January 2015, and Apple acknowledges that they have records also. However, the Executive Offices will not do anything other than have Senior technicians work with me.

Surely there is an answer other than switching to a PC to solve this problem. Please advise. Connie