Automatic transmission leaking

We inherited this car through my mother-in-law who can no longer safely operate it. Cosmetically the car is in new condition. The PO kept every single receipt for anything that was done to it from day one. The car was taken to the dealer throughout the warranty period and continued with the recommended service schedule included in the owner's manual. The car spent its entire life within a 30 mile radius of her home and was never hot rodded or abused. I seriously doubt it ever went over 60 mph until we picked it up in Beloit Wisconsin and drove it to Buffalo Missouri. (About a 10 hour drive at highway speeds of 55 to 70 mph)

Before we left all fluids were checked and were within recommended levels. Approximately two weeks afterwords the car started to slip the engage hard when accelerating from a stop. I immediately checked the transmission fluid level and found it was not even showing on the dip stick. I had to add 2.5 quarts of the recommended fluid as stated in the manual and it ran just fine. I checked it after every trip made for about 3 days and did not notice any changes. About 4 days later my wife took it on a 60 mile round trip when she returned I checked it and it has dropped to the point of not showing on the dip stick again.

I made a more detailed inspection under the car and found fluid coating the underside. It is not leaving puddles where its parked so I am assuming its leaking during operation. The highest concentration of fluid is to the rear of the transmission pan in the vicinity of the driver's side half shaft.

I am a fairly adept mechanic and am sure I can perform any repair myself regardless of its difficulty. I have not driven it or added any fluid to it yet, it is in my nature to do research on something like this before diving in and turning wrenches.

My question is more aimed at trying to understand what would have failed, and how could it have failed after only 40k miles and being taken care of so carefully? It has not even reached the time for its scheduled transmission filter change. Could it be something as simple as an axle seal or pan gasket? The pan itself is not oily. I really do not want to pull the transmission if it can be repaired in the car. In addition. We really need this car to be dependable and cannot afford an expensive repair.