SIM808 module restarting repeatedly
Check the datasheet and I think you will find you need 3 amps peak.  It requires this peak current when you make a call or send a text/sms.  

Use a 5A power supply and that should solve the problem.

I have never tried it but "super capacitors" might work, providing the extra power when its needed, it depends how long you need the 3A for.