Arduino Mega Serial USB not transmitting when receiving

Hi,
I am new to Arduinos and I am trying to make a Mega communicate with my computer via USB using Serial.

I am sending a command from the arduino to the computer every 500ms and receiving one back from the computer every 600ms.
Now, everything works fine on an Arduino Uno.
However, if I try and run the same code on a Mega, as soon as the computer starts transmitting every 600ms, the Arduino stops transmitting its own command.

The problem vanishes if I use a frequency higher that 800ms on the computer.

Any ideas on what might be happening???

Here's the code for your reference:

void setup()
{
  Serial.begin(115200);
}

void loop()
{
  Serial.print("Hi");
  delay(500);
}

Thank you very much,
Nick

This must work without a problem.You say this:

I am sending a command from the arduino to the computer every 500ms and receiving one back from the computer every 600ms.

void setup()
{
Serial.begin(115200);
}
void loop()
{
Serial.print("Hi");
delay(500);
}

Where in the code above you are implementing receiving messages from computer?

That's the thing: I didn't implement it at all but still the Mega stops transmitting if the frequency at which messages are sent to it is below 800ms!