I'm not sure what memory leaks you are talking about - there are many people using the Mono / Asp.net combination in production, and I'm sure they would notice if it were broken.
In any case, I cannot speak for ServiceStack, but there are no problems with concurrent connections to the Nancy host itself. I would recommend you put it behind nginx, which will do a great job of managing static content and will control the service using a supervisor.
Here's more info on setting up this wiki:
https://github.com/NancyFx/Nancy/wiki/Hosting-Nancy-with-Nginx-on-Ubuntu
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