Hmmm. Power steering system is isolated from engine.. so not getting burned off.
And youre sure theres no wetness under the vehicle.. from fluid being flung to the undercarriage?
How about the poeer steering cooler? Any wetness on it?
I had a 08 Saturn Outlook which I had to top off he P/S fluid within the first 10,000 miles due to it whining. I used solder seal fluid and never had to add any more. Fast forward about 110,000 miles or so when I had to replace the steering rack, when the mechanic opened up the boot on the rack, there was the fluid I lost 5 years before.
Also check the power steering high pressure hoses at the back of the engine (between the engine and the firewall) It's a metal / rubber hose. It should be completely dry. Otherwise the fluid could be leaking into the power steering accordion type boot that's on the steering rack. Squeeze those boots to check. The fluid has to be going somewhere. As rbarrios pointed out there is a power steering cooler at the front of the car , it may be leaking .. look at this video: