I've taken to leaving the machine running permanently, with BOINC running Einstein@home.

After a couple of days away, I came back to find the machine seemed to have rebooted and was waiting for a password to restart. The password got me past "logon", but there was no network connection and most software wouldn't run.

A full reboot restored things. A couple of days later, it did the same again. Watching more closely, I find that after a longish time, BOINC's icon disappears. At that point, trying to restart it or run any other program from the desktop brings the message "KLauncher could not be reached via DCOP." Only a restart will fix it.

Is there a fix, or is this a "feature"? Is the problem BOINC or Linux?

Pentium Coppermine 600MHz with Debian ("installed Knoppix 3.8.x")

have you tried leaving the machine without BOINC running ?
have you disabled power management etc ?

It's a desktop machine, and power management is turned off.

I notice that the HD light is permanently on and the machine extremely "busy" just before it goes into one of these states. I'm beginning to suspect BOINC, because I just caught it going into one, stopped BOINC, and it returned to normal.

I'll take a look at the BOINC site to see if anything's known there.