Running Exchange 2013 CU7 with Outlook 2007 utilizing standard settings:

IMAP Email from Outlook internal user or external user successful (usually) see below

From an application call by Security Information Systems product (Alarm Center)  It simply tries to send an attachment via a validated user, it is successful although quirky, sometimes it holds it a while then sends. Sometimes we get this error:  "The server responded: 421 4.4.2 Message submission rate for this client has exceeded the configured limit" and actually I just got that while sending an internal email to myself. So realistically IMAP also has some things to concern 

SMTP Email from Outlook internal user or external user successful

From application sends to internal just fine, the other day we had it sending to external but dropping off an attachment that will go with it.  Now it does not send at all, and nothing is left at the server even on the internal success. As I recall I could at least look it up and see that it left the server.

According to their support they tried my SMTP settings on their localized system (Alarm Control0 and it functions.  So I am stuck.

RECAP: IMAP flaky send "usually" complains a lot from app call

            SMTP was sending w/o attachment and was reflecting in server, now send "internally with attachment" but not externally, records no record of anything in server.

Just so you understand, IMAP doesn't send mail, it only retrieves it from a mailbox.  All mail for IMAP clients is sent via SMTP.  So it sounds like you can remove IMAP from this discussion completely.

Are you sending to the client submission port 587 or to generic SMTP 25?

Depending on which receive connector applies to these connections, you can modify the parameters to bump up the limits.  Check out the link below, maybe the parameter you're interested in is MessageRateLimit.

https://technet.microsoft.com/en-us/library/bb125140%28v=exchg.141%29.aspx?f=255&MSPPError=-2147217396

Thanks for that using port 25 as per their specs... I am thinking enable a 2nd SMTP connector with port 587 we do have an existing MX record pointing to a secondary (mail and mai2) which is acutually a disabled connector in there.   So a 2nd one exists now, I am presuming I could utilize that one change costing to 2 change port to 587 is this correct?

This system only sends a report receives no email

If the application authenticates, consider switching to 587 if the application supports it because it's likely the Client receive connector will do everything you need without modification.  You probably don't need a different connector.