I discovered this the hard way - repeated random reboots. Thought it might be the microdrive at first, but IBM indicated that microdrives were fine with running 24/7 (not even considered abuse for warranty purposes!) Swapping the drives didn't help, so I thought it might be a problem with the network adapter - since the reboots only ocurred when I had the remote window manager running.
Oddly enough, I have an IA-1 running at 400MHz (K6-III+ CPU) that has been running non-stop for quite a while, it was the "unmodified" IA-1 that had the problem. On a hunch, I scraped the goop from the CPU and and the heatsink, cleaned with rubbing alcohol, and used a regular heatsink compound. So far, so good. The system ran overnight with no problems.
Just a warning to those hackers who have been in their IA-1's a lot - you may want to consider preemptively replacing that green goop with something a bit more substantial.