I think it's really the lowpower.powerdown function that causes the issue. Just found out that after pressing the reset button the arduino will turn on immediately. So the time that passes during which the MCU doesn't come back on its own is probably the time needed for the board to do its own "reset" before it can be used again.
Plus a warning to everyone who wants to use the function: don't execute it right at the beginning of your sketch, i.e. right on start-up or just after a few seconds. If you do that there will be no time to upload a new sketch as the MCU will already be in sleep (or rather "coma") mode.
I was lucky I had about 40 seconds after which the function was executed - just enough time for a new sketch to upload. There are certainly methods to circumvent this problem but for newbies they will think they can trash their arduino.