Hello,
cPanel does not limit emails per hour for scripts sending email using the PHP mail() function or sendmail. Only SMTP authenticated emails are limited. Now, a sender rate per hour for ratelimiting could limit the emails, which would be caused by the person's IP having sent too many emails already. The only way to know for sure what is even happening would be to check the exim logs for the emails that aren't being received:
Code:
exigrep emailrecipient@domain.com /var/log/exim_mainlog
Where emailrecipient@domain.com is the email account that is not receiving the email.
If you do not have access to check the exim logs, please contact your hosting provider to ask for assistance.
Thanks!