An application started to log random error messages when trying to send emails through one of my Exchange receive connectors. So I checked and filtered the "Client Frontend" receive connector that showed at certain minute 6 email deliveries.

2016-01-12T17:49:00.530Z,EXCHANGESRV\Client Frontend EXCHANGESRV,08D31A7027871E90,3,10.20.20.5:587,10.10.6.10:59301,<,EHLO server1,
2016-01-12T17:49:00.811Z,EXCHANGESRV\Client Frontend EXCHANGESRV,08D31A7027871E90,43,10.20.20.5:587,10.10.6.10:59301,*,,Proxy session was successfully set up. Session for application1 will now be proxied

2016-01-12T17:49:01.155Z,EXCHANGESRV\Client Frontend EXCHANGESRV,08D31A7027871E92,3,10.20.20.5:587,10.10.6.10:59302,<,EHLO server1,
2016-01-12T17:49:01.421Z,EXCHANGESRV\Client Frontend EXCHANGESRV,08D31A7027871E92,43,10.20.20.5:587,10.10.6.10:59302,*,,Proxy session was successfully set up. Session for application1 will now be proxied

2016-01-12T17:49:01.764Z,EXCHANGESRV\Client Frontend EXCHANGESRV,08D31A7027871E94,3,10.20.20.5:587,10.10.6.10:59303,<,EHLO server1,
2016-01-12T17:49:02.014Z,EXCHANGESRV\Client Frontend EXCHANGESRV,08D31A7027871E94,43,10.20.20.5:587,10.10.6.10:59303,*,,Proxy session was successfully set up. Session for application1 will now be proxied

2016-01-12T17:49:02.343Z,EXCHANGESRV\Client Frontend EXCHANGESRV,08D31A7027871E97,3,10.20.20.5:587,10.10.6.10:59304,<,EHLO server1,
2016-01-12T17:49:02.593Z,EXCHANGESRV\Client Frontend EXCHANGESRV,08D31A7027871E97,43,10.20.20.5:587,10.10.6.10:59304,*,,Proxy session was successfully set up. Session for application1 will now be proxied

2016-01-12T17:49:02.921Z,EXCHANGESRV\Client Frontend EXCHANGESRV,08D31A7027871E99,3,10.20.20.5:587,10.10.6.10:59305,<,EHLO server1,
2016-01-12T17:49:03.171Z,EXCHANGESRV\Client Frontend EXCHANGESRV,08D31A7027871E99,43,10.20.20.5:587,10.10.6.10:59305,*,,Proxy session was successfully set up. Session for application1 will now be proxied

2016-01-12T17:49:03.499Z,EXCHANGESRV\Client Frontend EXCHANGESRV,08D31A7027871E9B,3,10.20.20.5:587,10.10.6.10:59306,<,EHLO server1,
2016-01-12T17:49:03.749Z,EXCHANGESRV\Client Frontend EXCHANGESRV,08D31A7027871E9B,43,10.20.20.5:587,10.10.6.10:59306,*,,Proxy session was successfully set up. Session for application1 will now be proxied

Then I checked and filtered my Exchange "Client Proxy" receive connector that showed 5 email deliveries and 1 error message:

2016-01-12T17:49:00.905Z,EXCHANGESRV\Client Proxy EXCHANGESRV,08D31A704B0F87A7,66,10.20.20.5:465,10.20.20.5:61643,*,,receiving message with InternetMessageId <892486179.161.1452620940960.JavaMail.tomcat@application1>
2016-01-12T17:49:01.014Z,EXCHANGESRV\Client Proxy EXCHANGESRV,08D31A704B0F87A7,67,10.20.20.5:465,10.20.20.5:61643,>,"250 2.6.0 <892486179.161.1452620940960.JavaMail.tomcat@application1> [InternalId=27504970564284, Hostname=EXCHANGESRV.bilbokoudala.lan] Queued mail for delivery",

2016-01-12T17:49:01.499Z,EXCHANGESRV\Client Proxy EXCHANGESRV,08D31A704B0F87AB,66,10.20.20.5:465,10.20.20.5:61649,*,,receiving message with InternetMessageId <1648812533.164.1452620941562.JavaMail.tomcat@application1>
2016-01-12T17:49:01.624Z,EXCHANGESRV\Client Proxy EXCHANGESRV,08D31A704B0F87AB,67,10.20.20.5:465,10.20.20.5:61649,>,"250 2.6.0 <1648812533.164.1452620941562.JavaMail.tomcat@application1> [InternalId=27504970564286, Hostname=EXCHANGESRV.bilbokoudala.lan] Queued mail for delivery",

2016-01-12T17:49:02.108Z,EXCHANGESRV\Client Proxy EXCHANGESRV,08D31A704B0F87AE,66,10.20.20.5:465,10.20.20.5:61658,*,,receiving message with InternetMessageId <238445017.167.1452620942165.JavaMail.tomcat@application1>
2016-01-12T17:49:02.218Z,EXCHANGESRV\Client Proxy EXCHANGESRV,08D31A704B0F87AE,67,10.20.20.5:465,10.20.20.5:61658,>,"250 2.6.0 <238445017.167.1452620942165.JavaMail.tomcat@application1> [InternalId=27504970564287, Hostname=EXCHANGESRV.bilbokoudala.lan] Queued mail for delivery",

2016-01-12T17:49:02.686Z,EXCHANGESRV\Client Proxy EXCHANGESRV,08D31A704B0F87B1,66,10.20.20.5:465,10.20.20.5:61677,*,,receiving message with InternetMessageId <81067270.170.1452620942738.JavaMail.tomcat@application1>
2016-01-12T17:49:02.796Z,EXCHANGESRV\Client Proxy EXCHANGESRV,08D31A704B0F87B1,67,10.20.20.5:465,10.20.20.5:61677,>,"250 2.6.0 <81067270.170.1452620942738.JavaMail.tomcat@application1> [InternalId=27504970564288, Hostname=EXCHANGESRV.bilbokoudala.lan] Queued mail for delivery",

2016-01-12T17:49:03.249Z,EXCHANGESRV\Client Proxy EXCHANGESRV,08D31A704B0F87B4,66,10.20.20.5:465,10.20.20.5:61690,*,,receiving message with InternetMessageId <635306337.173.1452620943315.JavaMail.tomcat@application1>
2016-01-12T17:49:03.374Z,EXCHANGESRV\Client Proxy EXCHANGESRV,08D31A704B0F87B4,67,10.20.20.5:465,10.20.20.5:61690,>,"250 2.6.0 <635306337.173.1452620943315.JavaMail.tomcat@application1> [InternalId=27504970564289, Hostname=EXCHANGESRV.bilbokoudala.lan] Queued mail for delivery",

2016-01-12T17:49:03.780Z,EXCHANGESRV\Client Proxy EXCHANGESRV,08D31A704B0F87B7,59,10.20.20.5:465,10.20.20.5:61698,>,421 4.4.2 Message submission rate for this client has exceeded the configured limit,

That error message was appearing everytime this application started sending multiple mails.
The problem was on the receive connector MessageRateLimit default value parameter.
There is a limitation of a number of messages that can be sent through the receive connector per minute:

[PS] C:\>Get-ReceiveConnector "EXCHANGESRV\Client Proxy EXCHANGESRV" | fl Name,MessageRateLimit

Name             : Client Proxy EXCHANGESRV
MessageRateLimit : 5

To change the parameter:

[PS] C:\>Get-ReceiveConnector "EXCHANGESRV\Client Proxy EXCHANGESRV" | Set-ReceiveConnector -MessageRateLimit 30

[PS] C:\>Get-ReceiveConnector "EXCHANGESRV\Client Proxy EXCHANGESRV" | fl Name,MessageRateLimit

Name             : Client Proxy EXCHANGESRV
MessageRateLimit : 30

And the problem is solved 🙂