TL;DR

Use raise; instead of  raise E;

Long version

In this code, when an exception caused by the ProduceMessage method got caught by the try … except construct and reached the Break statement in the Exception handler, an EAccesViolation occured:

procedure TProducerLoop.Run;
begin
  while True do
  begin
    Connect;

    while True do
    begin
      try
        ProduceOneMessage;
      except
        on E: Exception do
        begin
          Break; // app crashes here
        end;
      end;
    end;

    Disconnect;
  end;
end;

After many attempts to find the reason of the EAccessViolation, I found that it was caused by an raise E; instead of an raise; located in a method which got called by ProduceOneMessage. I removed the E and the EAccessViolation no longer occured.

function TBTMQProducer.InternalSend(const AMessage: IMessage;
  const Destination: IDestination;
  const CompletionListener: ICompletionListener): IMQProducer;
begin
  try
    Producer.Send(Destination, AMessage);
    CompletionListener.OnMessage(AMessage);
  except
    on E: Exception do
    begin
      CompletionListener.OnException(AMessage, E);
      raise E;
    end;
  end;
  
  Result := Self;
end;

References:

https://marc.durdin.net/2012/10/how-not-to-re-raise-an-exception-in-delphi/

https://zerolith.com/delphi/on-delphi-exception-raising-re-raising-and-try-except-blocks.html