beyond "try it", not really. Processing's stability depends on the stability of the JVM it runs in, and how well you wrote your code. If you have no memory leaks, it'll run as long as the JVM runs, which should run forever unless it's a poorly implemented JVM =)

I'd guess the hardware is the weak point.

make sure there's  a Uninterruptible power supply (or is it a laptop?)

Pomax and Chrisir make good points about memory leakage and ventilation / having a plan B. Run it for a while and log your framerate/memory usage just to be sure.

Thanks for the good feedback.

I'd be very interested in what you find. I installed a 9-6, 6 day a week for 4 month Processing openCV sketch recently. I did find that it slowed down and become more of a delay effect than immediate tracking. I used a webcam rather than kinect.
The sketch ran fine however otherwise. I wished I had set it to automatically reboot the computer after hours as sometimes it was not restarted at all I think- just the monitor turned off.

Do you have to run it at night also?

I would like to use the Kinect but have only just tried the new libraries which are very promising. I was using TUIO Kinect earlier and it crashed frequently.

Good luck with the installation and please post your findings. I am also interested if you are using the OpenNI or skeleton tracking libraries.

Best
Robbie