How to set Delay on GSM shield?
The SoftwareSerial receive buffer is getting filled up and discarding characters. You are not reading fast enough from the buffer. Adding Serial.println() will slow down your reading even more. The simplest solution to this is to increase the size of the SoftwareSerial buffer from its default size of 64 bytes to 256 bytes (or smaller, depending on what works for you). 

On a Windows PC, go to C:\Program Files (x86)\Arduino\hardware\arduino\avr\libraries\SoftwareSerial. Open SoftwareSerial.h and change the line:

#define _SS_MAX_RX_BUFF 64 // RX buffer size


to 

#define _SS_MAX_RX_BUFF 256 // RX buffer size


Save the file and try your sketch again.