hyper: Requests to hyper server eventually start failing.

I wrote a basic server application using hyper 0.9.10 that prints the IP, referrer, and body of each request to stdout (which I then redirect into a file):

extern crate hyper;
use std::env;
use std::io::Read;
use hyper::method::Method::Post;
use hyper::server::{Server, Request, Response};
use hyper::header::{Referer, AccessControlAllowOrigin};
use hyper::net::Openssl;

fn main() {

  let mut args = env::args().skip(1);
  let addr = args.next().unwrap();
  let cert = args.next().unwrap();
  let key  = args.next().unwrap();
  
  let ssl = Openssl::with_cert_and_key(cert, key).unwrap();

  let _ = Server::https((addr.as_str(), 443), ssl).unwrap()
    .handle(|req: Request, mut res: Response| {
      res.headers_mut().set(AccessControlAllowOrigin::Any);
      let _ = res.send(b"");
      if req.method == Post {
        let (addr, _, headers, _, _, mut body) = req.deconstruct();
        headers.get::<Referer>().
          map(|&Referer(ref referer)| {
            let mut buffer = String::new();
            let _ = body.read_to_string(&mut buffer);
            println!("{:}\t{:}\t{:}", addr, referer, buffer);
          });
      }
    });
}

Everything works as expected initially, but after some number of hours after starting the server, all requests to it begin to fail (and do so very slowly). When this happens, the results of time curl -k ... look like this:

curl: (35) Unknown SSL protocol error in connection to logbook.pyret.org:443 

real	1m43.616s
user	0m0.013s
sys	0m0.000s

Restarting the server application corrects this issue and requests are handled within 100ms, tops.

I’m flummoxed.