There are no limits within RDB ProNet to the number of emails that can be sent from a Mailshot. You may have a limit applied by your email service provider.
For example, some common defaults are:
Google G Suite has a limit of 2000 email messages per day.
Google Gmail has a limit of 500 email messages per day.
Microsoft Office 365 has a limit of 10000 email messages per day.
Microsoft Office 365 has a limit of 500 recipients for a single email.
Microsoft Office 365 has a limit of 30 emails sent per minute.
SMTP2GO paid accounts can send up to 3x their account limit.
We have recently seen from some clients who employ Office365 email accounts for emails generated by a mixture of portal registrations, submissions, etc (organic timing patterns) and batch jobs for things such as timesheet reminders and job alerts (bursts), are having emails fail seemingly randomly.
Microsoft is clearly making concerted efforts to prevent the use of their email services for bulk mail sending, by imposing strict sending limits, the details of which you can see at https://docs.microsoft.com/en-us/office365/servicedescriptions/exchange-online-service-description/exchange-online-limits.
We are currently advising affected clients that the best options for resolving this are to either use non-Office365 and less restrictive email accounts for these processes, or to employ a mail relay and let us have the relevant SMTP server details so that the processes connect to that relay instead of directly to Microsoft's servers.
We're not able to help with setting one up or recommending a suitable service, but your IT provider should be able to advise and assist; a number of clients have done this with immediate success once we've updated their database mail profiles to use their mail relays.
If you'd like to verify that the Office365 email accounts and their sending limits are indeed the source of the issue rather than your SQL server, for instance, you might want to test a non-Microsoft email account in place of your Office365 email account.