Thanks; it indeed was.
Does everyone using an external power source experience this? In other words, is it a known and confirmed "bug"?
Another question: Would it hurt to keep RX and TX connected to each other all the time I don't use them, to work around this?
yes it's a confirmed bug, and no, that would be a bad idea to connect them together, as you would possibly damage both the USB chip and the Atmega, since when the Atmega TX is low the USB TX could drive current into it, and vice-versa 
D