Yep, the Hertz rental on location rents them, but not sure if they have any limitations on mileage, etc. But we've had members rent themselves a Mini for events when their Mini was in for service or repair.
Beverly Hills Rent-A-Car also rents them, pretty pricey though. They have a couple locations here in Phoenix.
http://bhrentacar2.reachlocal.net/vehicle_info/125/0
I rented the first 2002 Mini I drove from National Rent-A-Car, but I don't believe they offer them anymore. Even then it was like $100 a day, and 100 miles max per day of rental. Anything over was like 25 cents per mile, to discourage any long distance drives... hehe.