It has to be an external dependency to the shell script - assuming what has been said is correct. That said, without seeing the script, cron is practically guaranteed not to be the problem. As the original wording of the question implies. The script is the problem. Please post the script.
@jim mcnamara.....I see where you are coming from but the OP says that the script was running fine and it's not been changed. Hence my question about how the crontab is being modified. If the crontab is being edited directly (not using the correct tools) then the change of time will not be noticed for up to 24 hrs unless the cron service is restarted.
We don't know the distro but on some the crontab update process is implemented separately and, if it's not running for some reason, the change of time will never get updated on the crontabs in memory.
So I agree with you that cron in itself is not the problem but how the change is being made could be.
My take was an external dependency. A lot of crontab files, like vixie cron, work correctly when editied by vi directly. Oldtime crond did not like that and would not notice a change for quite a while. Since we nothing to go on, I'm stuck.