Thanks - I was leaning towards something similar, though not so clear and precise. I had a DHCP address reserved for the gateway, to simplify access through the web interface; after the first times, I changed it to another address, thinking at it remaining busy, and lately simply removed the reservation, but nothing helped. By the way, I have also a long lease time that may give further complexity.
On the ESP8266 side, I expected that formatting SPIFF and reloading the sw would refresh everything, but maybe it is not. Now I could try to totally reset the router and see (not sure how it is different from switching off, but in this precise computer science we are used to these black magic rituals ).