If it’s the Raspberry Pi that stops responding that might be odd because the FAQ (http://www.raspberrypi.org/faqs) says the temperature for the AP is qualified from -40°C to 85°C and the LAN9512 is specified by the manufacturers being qualified from 0°C to 70°C. Both, directly from the FAQ.
Curiously, if you run it indoors for 24 hours do you experience the same lock up?
Edit: You could try something like this, http://hackaday.com/2012/06/26/adding-heat-sinks-to-a-raspberry-pi/