One idea I've toyed with before that I think is really interesting is the idea of having a persistent inbox but an offline processor
So think of it like this:
You have a queue that sits online with a webserver in front. The queue has some logic (the kind you can configure with RabbitMQ) for deduping and routing, but is still just a queue.
That's the only persistently online piece.
(@jenniferplusplus mentioned this earlier as well, this is not unique nor original to me as a thought)