I have designed a PCB which contains L80-R GPS and M95 GSM module. According to hardware design of M95, It can be supplied between 3.3V and 4.6V. However for my PCB if the supply below 4.3V I receive different kind of CME error every time like SIM card busy, SIM card not inserted or doesn't receive response to AT commands. You can see my M95, SIM card connector and supply schematics. BTW I am using a power supply not a battery or something like that.
Post the schematics of your PCB or at least a wiring diagram of how you wired the different components.