The ESP8266 can be set to deep sleep. You need to connect GPIO-16 with the RST pin to make this work. If you enable Sleep Mode, the ESP will go to deep sleep after the configured sensor delay setting.
When this state is active, you can't connect to the web interface. In fact, the ESP is turned off and only a dedicated timer circuit is still powered to wake up the main ESP core.
To keep the 'active time' as low as possible, when the ESP wakes up, it will immediately send the sensor data and go back to sleep. Not so easy to get it out of this wake/sleep loop.
But the ESP Easy can detect a cold boot situation and this is the only way to regain access to the web interface. So power off the ESP and reconnect power. You will have 30 seconds to connect to the Web interface and disable the Sleep Mode function.