There is always the possibility that this is a hardware issue, however, as long as the entry in the log is consistently the same program, so that has to be eliminated first. If it were never the same thing or no logs had any recent errorsin them then I would focus more on the hardware.
It is a hard lock though, not a soft lock; everything locks solid without indication as to what is causing it not even the mouse or any monitor moves. Not even the 3-finger salut does anything. And it is completely inconsistant as to when it will happen, for example the server has been up for over seven hours right now without incident. And then it might lockup solid every few minutes. I have replaced some hardware, (video card), and shuffled around where my USB mouse connector is, but nothing had any effect; nothing made it worse or better.
So, back to the issue of the logdaem entry in the POPUP.LOG. What does that program even do? I looked for some information on it, but there is very little within OS/2 itself on it, nor in any book that I have. The obvious answer is that it controls the logging of certain, (or all), log files that OS/2 generates, but that's just a guess. It may not be related to OS/2 itself, but something else running under the OS.
An easy test is to remove it from the CONFIG.SYS and see if anything different manifest. I think I'll give that a go.