Date & time goes off

You seem to be losing characters from the serial messages. Here is a test sketch that increments and prints a count every second. The header is sent so you can use the Processing sketch to view the output there to check it's the same as on the Arduino Serial monitor. If you don't see the numbers increase in sequence every second then perhaps there is some problem with your board or the serial connection.

#define TIME_HEADER  255 
unsigned long count = 1254422090;  // a starting count 

void setup(){
  Serial.begin(19200);
  pinMode(13,OUTPUT); // we flash the LED each second
}

void  loop(){  
   digitalWrite(13,LOW);  // first flash the LED
   delay(500);
   digitalWrite(13,HIGH);  
   delay(500);
   Serial.print( TIME_HEADER,BYTE);
   Serial.println(count);
   count = count + 1;
}