I'm having the same problem. Module 1 worked for a while, module 2 was provided with firmware straight out of the box, but I did not test it further.
Module 1:
The firmware can be reprogrammed, but it doesn't solve the problem.
The LED also turns blue if the wrong Wi-Fi SSID and password are entered, which is not what's expected (the LED should turn red!).
Module 2:
The firmware cannot be updated (I'm currently investigating this because the PICO D4 is soldered directly to a PCB; see also: https://forum.m5stack.com/topic/8007/serial-connection-problem-and-connection-to-server-failed).