I'm having exactly the same issue as described above with sim800L red module.
Attached is the schematics.
I have tried few modules and always the same result.
10-12 blinks and module resets itself
AT communication works fine.
LM is set to provide 4.2V and after diode i have 3.7V
I am using 5A power supply.
i have tried adding 2x470uF caps before modules but still no change.
EDIT:
After fiddling around i found that sim800's are very sensitive to the cable quality on power line.
So i replaced vcc and gnd connection cables on breadboard with good quality cable from power supply, suddenly all my problems are gone and sim800 works just fine and as expected.
