I've no reason to think that the patch I supplied here, some years ago now, was anything but a good idea, but it seems that my coworker Susi Berrington has found the real cause of my pain. According to:
https://github.com/systemd/systemd/issues/2039 (Change default value of RemoveIPC in logind.conf) ... systemd is removing fakeroot's IPC objects when the user performing the build, which in this case are happening under cron, programmatically ssh()s into the headless build machine to check on the build status. Argh! It's been more than a month since we stopped that from happening, a blissful month without failures.