If I have a websphere MQ topic and 3 listeners have subscribed to the Topic. One listener is down when a message comes in the Topic. Other listeners consume the message. When the listener comes back up, will the message still be there? My gut feel is no, but i cannot say for sure.
It is configurable, not by the topic but by subscriber. If you subscribe to a topic as a durable subscriber(all you have to do is set a flag and give a unique name) then you get all messages. Don't forget you have to unsubscribe when done or you have issues where the queue hold on to data forever and explodes. Relevant documentation.