Christian, Tomas, Thanks for your answers! I've been running 4.9.0-15-amd64 for the last few days and haven't observed anything untoward so far.
I guess the next step would be rebooting into 4.9.0-16-amd64 again to verify that it's still the kernel version making the difference. I'll mail my findings in a few days. -- Best regards, Ivan
