sterretje:
Your Mega has 4 serial ports; guess you changed the wrong one.If you redesign your software, there is probably no need to increase the buffer size. Have a look at serial input basics - updated. The trick is to regularly read the serial data.
Could you perhaps tell me where I can change the buffer size for Serial1? In HardwareSerial.h it doesn't mention any specific buffer sizes for the seperate ports...