My A/C Slowly Fades Out (Goes from Max to Off Over 10-15 Seconds)

I have an '05 Prius. I always turn off my AC before powering the car off. I used a sunshade. I don't turn on the AC for about a minute after starting the car and and/or getting up to normal speed. (about 35-40).

The AC will power on more reliably if on MAX. It will start to blow cold and stay on for about 45 seconds. Then, it starts to fade out and turns all the way off. If I allow it to wind all the way down, I can't turn it back on for about 10 minutes or longer. If I turn it off manually when it first starts to fade, the AC will allow me to turn it back on and get more cold air. (The problem is, I'd have to turn the AC on and off every 20 seconds or so to maintain cold air, and I'm not sure that's good for the car or battery...but I've done it before on my way to a wedding...didn't wanna be soaking wet for photos...and the air blew cold the entire 20 minute ride.)

I did discuss this with Toyota mechanics at dealership and they said it could be one of two problems. Problem one $1,000+. Problem two, $3,000+. But, diagnostic will be unrefundable $250 and I will just suffer through the Arizona summers for $3000. Problem is, I'll never be able to sell the car here w/o working AC.

Any advice would be greatly appreciated!!