The delay(10) calls in Client are maybe not long enough to received the response from Server, you should add something like :
int timeout = millis() + 5000;
while (client.available() == 0) {
if (timeout - millis() < 0) {
Serial.println(">>> Client Timeout !");
client.stop();
return;
}
Also, did you tried to put a delay between the GET and the POST ?
Because since the server is not multi-threaded, maybe the POST simply get lost.