Is your device sending data continuously?
You can check the buffer size of your serial port, but unless you have very strange hardware or modified the buffer size somewhere else, the buffer should be large enough.
I'm always very suspicious of any program that uses the "Bytes at Port" function. What does the data look like you are receiving? You have the termination character enabled as default. So if your device is sending a termination character, you should just read a large number of bytes and you'll receive a complete message at a time.
Better serial port protocols will use a command/response where you write a command to the device to tell it to send data, and only then does it return data. That way nothing is being sent until you are ready to read it.
I see you have XON/XOFF flow control set up. It is very rare to see that nowadays. Are you sure your device uses that also? I can see how incorrect flow control settings could mess up the buffer.