Sounds like a serialBuffer problem
What are you using to comunicate with the modem?(softserial , native UART,newsoftserial???)
The native serial support happens via a piece of hardware (built into the chip) called a UART. This hardware allows the Atmega chip to receive serial communication even while working on other tasks, as long as there room in the 64 byte serial buffer.
The problem could be you are not reading the incoming data fast anought and then the serialBuffer overflow
Post all the code