best meathod to capture serial data?

It is outputting raw measurement data for up to 32 channels. It is not NMEA strings but binary data.
I changed the code to read and output each byte in decimal format. Problem is it appears I am sometimes loosing a byte or two in the data stream along the way. This causes a big problem for me as there is no way to determine along the way which segments are complete and which are missing a byte unless the entire message is recieved and the position in the array of the end byte pair can be found. Then I'm not certain how to go about sorting the rest.
I have the baud rate at 115200. Is it possible the device is sending bytes faster than the ATMEGA2560 can read them from the buffer?