muneeb It's hard to assist you here. The most obvious reason of the problem is the processing of MQTT message on your side or network connection I/O processing by the mqtt client library.
So the very first question will be - what library are you using?
Next thing to do is to eliminate library error from user-level error.
First create empty handler for the message and check if such kind of client connections are OK. If not - you have an error with library.
If you were OK on previous stage, create a handler with 0.1-1 second sleep - if your code is synchronous - the delay should be quite small to be able for the code to handle all messages. And check how it is going. If you have problems - either delay is too large or the processing of network I/O in your library is not good.
In al other cases the problem will lay to your original handler - e.g. your message processing code.
Just to ensure that broker operates good - create a few sessions using https://mqttboard.flespi.io - their handler will just output message into browser. If for any reason you have problems there - please immediately contact flespi team via chat button in top-right corner of your flespi.io. Sometimes we discover gnomes in datacenter between racks and they do some magic things. Hope it is not your case.
And yes - for most of your questions above the answer is NO. This is just simple MQTT Broker, nothing more. By the protocol there is no retransmit packet command - client should just close the connection if anything went wrong.