This thread was helpful to me, as i just tried to setup a Shelly 1PM that I purchased a couple of weeks back and the factory firmware was still on firmware 20191219-114622/1047-long-id-for-shelly-devices@d05667c7 from the factory. I had wired up the 1PM with just the live and neutral wires to set up the wifi. All was good for the first five minutes, it showed the webinterface after entering the WPA key within seconds. But then it would not respond to the webpage calls anymore.
Interestingly, the REST API did work intermittently. I tried to /reboot the device but that gave no response, but when added gibberish behind the /reboot command like /rebootasldkfjalsfjijlsadkfjalskdjf..etc, it gave an OK JSON response? Rebooting the router did help to get the webinterface back, but it would not respond after a few minutes again.
After that I tried to update the firmware via the REST api. That turned out not to work because the archive.smarthome-forum.eu webservers was so heavily loaded that the download timed out on the 1PM. So I downloaded the firmware separately and hosted it locally. After that the firmware update was successful.
I did not enable a static IP on the 1PM, my AVM Fritz!Box 8753 and AVM Fritz!Repeater 3000 were to take care of that. Interestingly, the 1PM signed up to the repeater, which is located on the first floor, instead of the Fritz!Box in the same room.