HttpListener with SSL certificate hanging on GetContext()

I've created a windows service which uses a HttpListener to respond to some third-party requests using .NET Framework 4.0. The listener is bound to a https prefix via the following:

listener.Prefixes.Add("https://+:" + Properties.Settings.Default.ListeningPort.ToString() + "/");

The service also self registers the https certificate in the computer store via:

X509Certificate2 certificate = new X509Certificate2(Properties.Settings.Default.HttpsCertPath, "", X509KeyStorageFlags.MachineKeySet);
X509Store store = new X509Store(StoreLocation.LocalMachine);
store.Open(OpenFlags.ReadWrite);
store.Add(certificate);
store.Close();

Further more, the service also registers the certificate - ip:port binding in Http API using the following:

ProcessStartInfo psi = new ProcessStartInfo();            
psi.FileName = "netsh";
psi.Arguments = "http add sslcert ipport=0.0.0.0:" + Properties.Settings.Default.ListeningPort.ToString() + " certhash=" + certificate.Thumbprint + " appid=" + appId;
Process proc = Process.Start(psi);                
proc.WaitForExit();
psi.Arguments = "http add sslcert ipport=[::]:" + Properties.Settings.Default.ListeningPort.ToString() + " certhash=" + certificate.Thumbprint + " appid=" + appId;
Process proc = Process.Start(psi);
proc.WaitForExit();

Everything works well, as expected... EXCEPT... (and here comes the EVIL part): After running for some time, an hour or so, listener.GetContext() no longer returns and the clients get dropped with a "connection reset" like error.