I've been having a terrible time trying to get my A6 "mini" module (not the same as the older larger modules) to respond reliably - and I'm just trying to talk to it via a terminal and a USB FTDI TTL serial widget. I ended up buying a second A6 mini thinking the first was faulty, and had the same troubles.
After some tedious multi-day experimenting, here's what's been working for me lately:
A) Attach FTDI adapter (set to 3V3) to serial pins
B) Apply power to the module (not sure why 2A adapter is required - mine pulls 0.2A max - maybe it will need a fat capacitor on there later)
C) (Sometimes not needed:) Pull the RESET line HIGH (not LOW) for 3-4 seconds with a 1K resistor to 5V - NOT DIRECTLY TO 5V. (A reset direct to 5V makes the unit unstable/unresponsive after the restart, though it doesn't seem to do any lasting damage.)
D) Immediately start pinging the unit with "AT\r" until it responds "OK", and keep pinging it (like once a second) until after initialization is completed - if you don't, it will ignore all further input.
If you can't get a response, go back to C.
I'm starting to think my A6 isn't getting a clean reset on power-up due to the serial input still being connected/powered, but a reset with a 1K resistor seems to overcome that.
I've tried resets with a 10K and a 1N4004 diode (to drop to ~4.2V), but they aren't reliable.
I've got a SIM800L module on a board here also, and it's a lot easier to get talking - though they've screwed up the pin spacing for insertion into a 0.1" breadboard - the left/right rows of pins are 0.85" apart, rather than 0.9" - which is just stupid.