Oversimplified method of sending ThingSpeak updates from Spark Core. (Not really recommended for real world use.) This connects and sends data successfully several times, but eventually something hangs and it stops updating.

gistfile1.txt

// ThingSpeak Settings
char thingSpeakAddress[] = "api.thingspeak.com";
String writeAPIKey = "THINGSPEAK_WRITE_KEY";
const unsigned int updateThingSpeakInterval = 30000;   
// Variable Setup
unsigned long lastConnectionTime = 0; 

// Initialize TCP Client
TCPClient client;

void setup()
{
  // Start Serial for debugging on the Serial Monitor
  Serial.begin(9600);
  delay(1000);
  Serial.println("Setup complete");

}

void loop()
{
  // Read value from Analog Input Pin 0
  String analogPin0 = String(analogRead(A0), (unsigned char) DEC);
  
  // Update ThingSpeak
  if(!client.connected() && (millis() - lastConnectionTime > updateThingSpeakInterval))
  {
    updateThingSpeak("field1="+analogPin0);
  }else{
      delay(500);
  }
  
}

void updateThingSpeak(String tsData)
{
  if (client.connect(thingSpeakAddress, 80))
  {         
    Serial.println("Sending TS update: "+tsData);
    
    client.print("POST /update HTTP/1.1\n");
    client.print("Host: api.thingspeak.com\n");
    client.print("Connection: close\n");
    client.print("X-THINGSPEAKAPIKEY: "+writeAPIKey+"\n");
    client.print("Content-Type: application/x-www-form-urlencoded\n");
    client.print("Content-Length: ");
    client.print(tsData.length());
    client.print("\n\n");

    client.print(tsData);
    
    lastConnectionTime = millis();
    
    delay(2000);
    
    // Just ignore return info for now
    Serial.println("Disconnecting");
    client.flush();
    client.stop();
    
  }
  else
  {
    Serial.println("Connection to ThingSpeak Failed--disconnecting");   
    client.stop();
  }
}