Following what damago1 found:
- IDE is initiating the auto-reset of the Leonardo (using the serial port selected in the Tools > Serial Port menu). It does it by opening the virtual com port at 1200 baud and then closing it. This is a signal for firmware to reset the processor of Leonardo, and the virtual (CDC) serial/ COM port disappears from the list.
- the Arduino software waits for a new virtual (CDC) serial / COM port to appear - one that it assumes represents the Leonardo bootloader. It then performs the upload on this newly-appeared port.
I can guess the port should change for the serial monitor too, but I don't know how the official one works if I don't see any difference in these routines and I don't know how to replicate the Leonardo behavior with another board to test, so for the moment I can't do anything to fix this.