First of all: Many thanks to all members, great work !
This problem is reproducible (for me):
Doing exactly the steps from “Getting started” (with the goal not to plug in keyboard / monitor and only to ssh into)
change dietpi.txt (WIFI only):
AUTO_SETUP_NET_ETHERNET_ENABLED=0
AUTO_SETUP_NET_WIFI_ENABLED=1
Open dietpi-wifi.txt on a WIN10 PC with wordpad (but in another try with notepad):
Change aWIFI_SSID[0]=‘MySSID’ and aWIFI_KEY[0]=‘MyWifiKey’
of course with my own SSID / Key 
and so on …
Finaly I’ve plugged in SD card, to have a nice time while dietpi and Rpi0 were both working very hard.
But after a while there was no ping (and putty can’t login) and router doesn’t show anything new.
Not amused I search another keyboard and another monitor and take a look at console.
ok. I found in dietpi-wifi.db:
SSID as well as the WLAN Key both were corrupted by an ending carriage return.
I reset SSID and WLAN key with dietpi-config manually and finally Rpi0 was connected to my WLAN.
Doing some research on dietpi/func/dietpi-wifidb and shrinking the bash script to seven lines for testing:
#!/bin/bash
i=0
aWIFI_SSID[$i]=’’
. ./oo
cat << EOF | od -bc
aWIFI_SSID[$i]=’${aWIFI_SSID[$i]//’/’\’’}’
EOF
run this with an also shrinked dietpi-wifi.txt named oo
(simulating partially bash script dietpi-wifidb on it’s first run):
./oo.sh
0000000 141 127 111 106 111 137 123 123 111 104 133 060 135 075 047 166
a W I F I _ S S I D [ 0 ] = ’ v
0000020 145 162 171 123 145 143 162 145 164 120 141 163 163 167 157 162
e r y S e c r e t P a s s w o r
0000040 144 015 047 012
d \r ’ \n
0000044
( od -bc oo shows no \r inside the plain text of oo )
Same with aWIFI_KEY[].
Hey DietPi, I’ve a verySecretPassword but there is no carriage return at the end at all
So a workaround for me could be to kill first all carriage returns from my dietpi-wifi.txt before
transfering my new sd card to the Rpi0 and before taking a cup of coffee.
But perhaps it’s a bug in dietpi/func/dietpi-wifidb in the bash pattern substitution construction (above).
Did I already mentioned: many thanks to all in the team, great work !