Tell us more about your:
1.) System - for instance, is your RAID 0 your only drive, i.e. your system drive? More details will help.
2.) Assets - details on your HD material. The more, the better.
3.) Project - what Presets are you using?
To potentially find some clues to the crashes, see this ARTICLE. It'll get you started along the path. Maybe no hard answers, but you'll be able to rule out some things, and might get enough of those clues to help.
Yes, the RAID 0 is the only hard drive on the system. I also have a ATI Radeon HD 3870, driver version 8.510.0.0, with 512mb memory. The video was shot on the Canon XH A1s in the 1440 x 1080, 30f mode. The project I'm working on now has over 100 videos and is about 15 minutes long. I'm using the HDV 1080P30 preset in Premiere.
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Using a RAID 0 as a system drive is not the best practice. Besides the potential for a systemic crash, should one disc fail, a better use would be two (ideally a minimum of three) physical HDD's.
Though the RAID 0 will give you a little more speed, the OS sees it as one disc, and when trying to access it for many operations will often encounter bottlenecks, especially with HD material.
Harm Millard has done an excellent ARTICLE on I/O sub-system setup for an editing rig. Lot of useful info there.
Now, your I/O might not be the cause of the crashes, but would be a possible candidate.
What did you find in Event Viewer? Anything useful there? Do not forget to follow all links in all error and warning messages. Read the links especially, though there will be a lot of useless "stuff" in many of those messages.