[mgmueller]

Just promptly have received response from iRex:

"The on/off switch is a multifunction button and so there is a considerable difference in how long you hold the switch to the left.
To turn the DR800 off please slide and hold the on/off switch to the left for 2-3 seconds. By sliding the switch to the left for 5 seconds you will reset the device."

That's exactly, what the manual says.
And I thought, I had figured it out.
But the last few times, I only made it to standby - or accidentally to reset.
My guess was, the first times when I thought I'd switched it off, I just went into standby. Then I accidentally did the reset and mistook this for booting from off.
Now I'm not sure, what to think. Anyway, I can't turn it off (anymore) and asked iRex again for confirmation.