Hi there. It seems to me that your issue is likely to be ROM related. Is your nexus one rooted? If so, are you running a custom ROM such as cyanogenmod?Random reboots are primarily attributed to ROM or kernel problems. Have you installed a custom kernel?

I am having the a similar problem. But after extensive trouble shooting trying CM and few other roms I found the problem is hardware related.

With the nexus one switched on remove the battery cover, now but the phone facing towards you try pressing with your fingers just under the power button where the speaker is. Try pressing just around that area with your fingers around that area. You might find a spot where it will reboot every time you touch it.