Ouch, I've never encountered this, but I'll tell you my gut feel and maybe you can get somewhere with this. (Thanks for reporting it on the Github issue tracker).
So unicorn is OK, but thin and webrick are not, mmmm.
My guess is that the working directory used by the daemon process for thin and webrick is not Rails.root. You might want to try debugging this line in rack-zippy to see what the path is being searched for the asset file: https://github.com/eliotsykes/rack-zippy/blob/master/lib/rack-zippy.rb#L87
rack-zippy since version 1.1.0 (which you're probably using if you're using the latest Gem) passes all requests it can't find a file for on to the remaining middleware stack.
In development+daemon mode, rack-zippy will be passing the request onto the asset pipeline, so I think we can assume that the asset pipeline has no problems with daemon mode.
In production+daemon mode, the asset pipeline is probably disabled (as you'd want), and rack-zippy will be passing the request onward if it can't find the asset file (which is probably the case if the working directory is not Rails.root), and then the remaining middleware will give you the routing error you see.
If you enabled the asset pipeline in production (very much not recommended), then I would expect the routing error would disappear, and rack-zippy would not be doing anything useful.
Sorry I don't have anything more solid for you to go on.