Thanks for your comments! Yeah, these connectors ... best would be to avoid them. But this time, they weren't the reason. The power-cable to the AQ was my first thought, too. So I moved it and touched the connector with the AQ powered. No problems, no intereruption.
I still don't think that it is a general problem of 4S or with the AQ! It seems to be an isolated case so far.
I worried a little bit about feedback coming from the esc or induction in the signal-cables. But everything seems to be clean.
@Jussi: thank you for the offer, here is a Logfile of the copter strapped down, 4S, with a non-responding AQ in the end with motors still running (logfile must have ended long before I cut the power).
https://depot.uni-konstanz.de/cgi-bin/e ... d9ypspzsm2
EDIT: One thing I forgot to mention: Today I checked the PWM-outputs, the Voltage-in and the 5V of the AQ board with an oscilloscope while running: nothing conspicuous. Nice PWM-signals, clean voltages. No spikes at all.