Reaper -a restart causes app to hang

I’ve looked through the archive to see if anyone else has encountered
this, but didn’t find anything. The short version is, when I use cap
deploy (and thus reaper -a restart implicitly), my app stops
responding. I’ve verified that using reaper in graceful, reload and
exit modes works as intended. The weird thing is, I watch the logs
and see that my request is going through, but the page never
returns. This leads me to believe that there’s something goofy in
how the connection to lighttpd is made.

To make it even stranger, if I sit there in the browser and reload N
times where N is the number of dispatchers, I can kick it out of
whatever state it’s in. I suppose I could just do that every time,
but surely there’s a better way. Anyone else seen this behavior?
Deploying to a dedicated RedHat Enterprise Linux box.

K