This is a hardware problem.
We have experience the same issue in the company I'm working for and after a short discussion with a SimCOM Engineer we conclude it was a soldering issue. The problem may lies in the PCB or inside the SimCOM module. In both cases some part/parts are not soldered or the solder contact is broken. If the problem is outside you may fix it by inspecting the parts. If it is inside the SimCOM module there are very little you can do with the usual tools.
Just to be clear I quote a little bit of the discussion
Original question to SimCOM:
A)We apply a zero pulse to PWR-key pin as you can see in the channel-1(yellow line)
and immediately the SIM800c module wakes up, the net and status led pins
become active (one led on the other blinks).
B) After a short time <1.5sec the SIM800c deploy a signal to SIM_VDD pin
(channel-2 - blue line)
Now in some boards the SIM_VDD pin goes to 1.8V as it appears in the
first of the 4 pulses and stay there. This situation is true if there is
a SIM card in the slot and the SIM800c is working properly. In that case
we can proceed and register to the network, send SMS etc...
In some boards though, as you can see in the screenshots, the SIM800
seams not to recognize the SIM card and tries again with 2 more pulses in
3V and one last one in 1.8V. The behavior is like there is no SIM-card in
the slot. Just to be clear. The SIM card is the same in all tests.
VBAT=3.9V, SIMVDD produced fine at 2.8V etc... The boards are identical
and no further code with AT commands is running.
Quite final answer from SimCOM:
It must be a soldering issue then. Did they followed recommended Solder
https://www.elecrow.com/download/SIM800C_Hardware_Design_V1.02.pdf page 46
Please ask them where they measured signal from the scope pictures. From
the SIM card pins? If no, can they repeat that on them and send pictures.