I've had, on occasion a problem with processes becoming zombies instead of terminating when they're finished:

zak@orionrecruitinggroup:~$ ps -A|grep defunct|wc -l
     145

Killing all the zombies doesn't solve the problem because new ones are generated constantly. They eventually cause mysql to act up; most services on the system depend on mysql. The only solution seems to be a reboot, which isn't acceptable to do regularily on a machine that needs to be available to receive mail all the time. The symptoms are similar to this.

Has anyone encountered a similar issue?

Discussion that you referenced was continued here: http://seclists.org/lists/linux-kernel/2004/Apr/2065.html, where it is described as a local DoS. The symptoms are ascribed to a userspace program blocking a signal and then receiving many such signals, causing sigqueue overflow.

When sigqueue overflows in 2.4, all linuxthreads-based programs, including root-run daemons, stop receiving notifications about thread exits. All completed threads become zombies.

In 2.6, since NPTL is used instead of linuxthreads, there are no zombies from system daemons but sigqueue overflow still causes strange (bad) things to happen.

They specifically mention mysql problems.

Edited to add:

More specifically, long lived processes that generate many short-lived threads during their normal operations (like mysql) are the first to feel the pain when the process table fills up.

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/ Peter