It looks like you are using Direct Messaging and are hitting the rate limits of your system. There will be lost messages when your system cannot send or receive fast enough.
What are the size of your messages? For a saturated 1Gbps link, your message size would be something like
1000 * 1000 * 1000 / 8 / (264/2.8) / 1024 ≈ 1.2KB
If you are using PERSISTENT delivery mode for sending messages and receiving them with an endpoint, there would not be any lost messages. You can refer to the tutorial on Guaranteed Messaging
http://dev.solacesystems.com/docs/core-concepts/#message-delivery-modes, especially on message promotion and demotion. If you're using JMS, having the direct-transport property set to "true" and default-delivery-mode property set to "non-persistent" will result in DIRECT delivery mode.
There are keep-alive mechanisms on both sides of the appliance and the API layer, where the default interval is 3 seconds. This prevents connection breaks even when there were no messages. Reconnection happens automatically at API, if set. These reconnect, keepalive settings can be found both in the client-profile or JMS Connection Factory (appliance side) and the API side. See
There is no "max messages per session" or similar setting. That simply doesn't make sense.