Rx light on FTDI board is constantly on when computer sleeps.

I am using an FTDI board to upload sketches to an Arduino chip on a breadboard.
I have a sketch that periodically (every 5 minutes or so) sends messages to the computer it is connected to and it works fine when the computer is on. Sometimes I put the computer to sleep because the computer still provides power through the USB port and thus the project still runs. But the next time the Arduino sends the update message, the Rx light on the FTDI board is on constantly. It turns off immediately only when I bring the computer back on from sleeping.

The code on the Arduino has not halted as I can see that in the message it sends since I count the minutes it has been running and send that in the message.

I have been speculating about it and I thought it was because it fills the buffer of the FTDI chip and since there is nothing receiving the data it keeps it in the buffer only to be overwritten as more data gets sent from the Arduino to the FTDI board. But then it should also behave like that when I do not have the serial monitor open.

My question is why does it do that?