You can enter the 'Zombie mode' reproducibly by pulling GPIO-2 to GND. When the chip wakes up from deep-sleep, you are in 'Zombie mode'.
Pull it to VCC and you won't enter Zombie mode anymore on wake-up.
This seems to be some undocumented feature (or bug) of the chip. Pull GPIo-2 to GND while powering on or do a reset always enters this mode.
My system now seems to work reliable w/ the GPIO-2 pulled to VCC. Time will tell.
There maybe more floating pins around that need to be brought into a reliable startup state. I can imagine that it also may be a good idea to pull up RST/GPIO-16.