Comment 10 for bug 358573

That worked out well. I have added these jobs to my crontab:

*/1 * * * * /bin/ls >/dev/null
*/2 * * * * /bin/ls >/dev/null

Therefore every two minutes both jobs are run, while every other minute only one of them gets started.
Output from monitor_private_dir.sh since then:

Mai 19 11:44:27 ~/Private was unmounted.
Mai 19 12:28:27 ~/Private was unmounted.
Mai 19 12:32:27 ~/Private was unmounted.
Mai 19 12:33:27 ~/Private was unmounted.
Mai 19 12:36:27 ~/Private was unmounted.
Mai 19 12:42:27 ~/Private was unmounted.
Mai 19 12:46:27 ~/Private was unmounted.
Mai 19 12:52:27 ~/Private was unmounted.
Mai 19 12:54:27 ~/Private was unmounted.
Mai 19 13:00:27 ~/Private was unmounted.

At 12:33 another regular cronjob was running, so that uneven hit doesn't count. Every other hit proves the theory that two arbitrary cronjobs have to have the same start time to raise the chances of provoking the unmount of ~/Private.

Are you able reproduce the bug with this test case (adding the two lines to your crontab and interactively running my script)?