By default the Magento application settings are such that when cron.php is being processed for a period longer than 15 minutes after a job was supposed to be completed, it is marked as missed and is ignored. This setting is under System > Configuration > System > Cron > Missed If Not Run Within.

That is why you need to change this setting to a value greater than 30 minutes. For example you can set it to 35 minutes. Otherwise tasks that are only scheduled once a day or so will get marked as missed.

After that set Schedule Ahead for to 35 and the cronjobs issue should be resolved. You can check the Magento cron log by visiting:

http://YOURDOMAIN.COM/cronmon.php