Cron.hourly:

[root@praesto1 cron.hourly]# ls -la | more
total 12
drwxr-xr-x 2 root root 4096 Jan 3 2002 .
drwxr-xr-x 59 root root 8192 Nov 25 08:16 ..


Cron.Daily:

[root@praesto1 cron.daily]# ls -la | more
total 44
drwxr-xr-x 2 root root 4096 Nov 6 13:12 .
drwxr-xr-x 59 root root 8192 Nov 25 08:16 ..
-rwxr-xr-x 1 root root 276 Jun 24 2001 0anacron
-rwxr-xr-x 1 root root 51 Sep 4 2001 logrotate
-rwxr-xr-x 1 root root 402 Aug 31 2001 makewhatis.cron
-rwxr-xr-x 1 root root 104 Sep 6 2001 rpm
-rwxr-xr-x 1 root root 132 Oct 24 2002 run_nohup.sh
-rwxr-xr-x 1 root root 132 Jun 24 2001 slocate.cron
-rwxr-xr-x 1 root root 91 Aug 13 2001 sysstat
-rwxr-xr-x 1 root root 193 Nov 28 2001 tmpwatch

Cron.Weekly:

[root@praesto1 cron.weekly]# ls -la | more
total 20
drwxr-xr-x 2 root root 4096 Nov 6 13:12 .
drwxr-xr-x 59 root root 8192 Nov 25 08:16 ..
-rwxr-xr-x 1 root root 277 Jun 24 2001 0anacron
-rwxr-xr-x 1 root root 399 Aug 31 2001 makewhatis.cron

Cron.Monthly:

[root@praesto1 cron.monthly]# ls -la | more
total 16
drwxr-xr-x 2 root root 4096 Nov 6 13:12 .
drwxr-xr-x 59 root root 8192 Nov 25 08:16 ..
-rwxr-xr-x 1 root root 278 Jun 24 2001 0anacron

Last time you did that, gpm was already running. Do..
killall -9 gpm
rm /var/run/gpm.pid
Then try the strace again.
This time it should show what it's missing.

New Output....

execve("/usr/sbin/gpm", ["gpm"], [/* 51 vars */]) = 0
uname({sys="Linux", node="praesto1", ...}) = 0
brk(0) = 0x805a500
old_mmap(NULL, 4096, PROT_READ|PROT_WRITE, MAP_PRIVATE|MAP_ANONYMOUS, -1,
x40017000
open("/etc/ld.so.preload", O_RDONLY) = -1 ENOENT (No such file or dire
open("/etc/ld.so.cache", O_RDONLY) = 3
fstat64(3, {st_mode=S_IFREG|0644, st_size=69846, ...}) = 0
old_mmap(NULL, 69846, PROT_READ, MAP_PRIVATE, 3, 0) = 0x40018000
close(3) = 0
open("/lib/i686/libc.so.6", O_RDONLY) = 3
read(3, "\177ELF\1\1\1\0\0\0\0\0\0\0\0\0\3\0\3\0\1\0\0\0@\307\1"..., 1024
4
fstat64(3, {st_mode=S_IFREG|0755, st_size=5779542, ...}) = 0
old_mmap(NULL, 1291464, PROT_READ|PROT_EXEC, MAP_PRIVATE, 3, 0) = 0x4002a
mprotect(0x4015c000, 38088, PROT_NONE) = 0
old_mmap(0x4015c000, 24576, PROT_READ|PROT_WRITE, MAP_PRIVATE|MAP_FIXED,
1000) = 0x4015c000
old_mmap(0x40162000, 13512, PROT_READ|PROT_WRITE, MAP_PRIVATE|MAP_FIXED|M
YMOUS, -1, 0) = 0x40162000
close(3) = 0
munmap(0x40018000, 69846) = 0
brk(0) = 0x805a500
brk(0x805a680) = 0x805a680
brk(0x805b000) = 0x805b000
open("/var/run/gpm.pid", O_RDONLY) = -1 ENOENT (No such file or dire
open("/dev/tty0", O_WRONLY) = 3
ioctl(3, 0x541c, 0x8056fa0) = 0
close(3) = 0
fork() = 1830
_exit(0) = ?

That's wierd... well it dies, but that didn't write to the log file at all
My only suggestion is to recompile the newest gpm, or to get the rpm for it.

# run-parts
01 * * * * root run-parts /etc/cron.hourly
(etc)
Is it me or do the times look a bit wonky? I mean (running Vixie-cron) I always thought the fields where: "minutes, hours, day of month, month, day of week"? Not that it will help you solve your problem, but the times they're run at look weird.

If you can verify the contents of the other cronjobs are "sane" by your standards, then at least you can say your problem probably hasn't got to do with one of these. Only thing I can't recognize is the /etc/cron.daily/run_nohup.sh, but then it's run at such a time it couldn't be part of killing the box.

Definately weird problem, especially because of the period you mention.
Doesn't sysstat show wierd fluctuations in CPU or memory usage over that period?