concurrent requests (Rook, but I think the question is more general)

This question involves Rook, but I think the answer will be general enough
that it pays to post here. At any rate, I don't know enough to know whether
this is a Rook only issue or a general R issue.

Here's what I'd like to do (and indeed, have code that should do this):

1. Start R, Rook
2. Start an analysis via a HTTP request to Rook. This analysis uses .Call()
to some compiled C code, if that matters. The C code calls a callback
function to update a variable with its progress.
3. While the analysis is happening, use Rook to obtain current status with
an HTTP request

The problem is that once the analysis starts, Rook does not respond to
requests. All of the status requests to Rook pile up, and then are answered
when the analysis (step 2) is done. Here is some example code to demonstrate
what the issue:

##########

library(Rook)
s <- Rhttpd$new()
s$add(
  name="pingpong",
  app=Rook::URLMap$new(
    '/ping' = function(env){
      req <- Rook::Request$new(env)
      res <- Rook::Response$new()
      res$write('This is ping.')
      Sys.sleep(20)
      res$finish()
    },
    '/pong' = function(env){
      req <- Rook::Request$new(env)
      res <- Rook::Response$new()
      res$write("This is pong.")
      res$finish()
    },
    '/?' = function(env){
      req <- Rook::Request$new(env)
      res <- Rook::Response$new()
      res$redirect(req$to_url('/pong'))
      res$finish()
    }
  )
)

s$start(quiet=TRUE)
s$browse('pingpong')

#############################

If you request /ping, R runs Sys.sleep() for 20 seconds. This is where my
.Call() statement would be. While the .Call() (Sys.sleep()) function is
doing its thing, I need to get Rook to respond on /pong (which would simply
respond with the progress), but if you run this code, request /ping, then
immediately request /pong, you'll see that the /pong request will not be
answered until the Sys.sleep() is done.

Of course, for a progress report to be useful, the requests have to be
answered immediately. Is this a Rook issue, or an R issue? Or am I asking
something unreasonable?