A few days ago the oom_killer killed the sshd on my QNAP NAS, so I had to hard-reboot it. Following that, I uninstalled the v4 kernel and reinstalled the v3 kernel that had previously been installed from jessie-security. The machine is now back to running its same workload now without any messages to dmesg or /var/log about memory.
No other software, including libc, has changed on the system. It seems pretty clear I won't be able to use a v4 kernel on this hardware because something has changed in its memory management. I believe it's a bug for a new kernel to behave differently under the same workload on the same hardware.
