Beginning with MS Exchange 2010 Microsoft implemented a feature called "Throttling Policy" which control the "MessageRateLimit" as explained here:
The MessageRateLimit parameter specifies the number of messages per
minute that can be submitted to transport. For messages submitted
through the Mailbox server role (using Microsoft Outlook, Microsoft
Office Outlook Web App, Exchange ActiveSync, or Exchange Web
Services), this results in the deferral of messages until the quota
for the user is available. Specifically, messages appear in the Outbox
or Drafts folder for longer periods of time when users submit messages
at a rate greater than the MessageRateLimit parameter.
For POP or IMAP clients submitting messages directly to transport
using SMTP, clients receive a transient error if they submit at a rate
that exceeds the MessageRateLimit parameter. Exchange attempts to
connect and send the messages at a later time.
So please follow the article here, build a new Throttling Policy an assign that to the users who should be able to send more emails.
Please do NOT change the default throttling policy.