In case someone still needs help with this issue, check this project where I made 4 RFID readers work simultaneously without any problem : GitHub - Annaane/MultiRfid: Multiple RFID readers System with Arduino.
P.S: Whenever I got the error "Communication failure, is the MFRC522 properly connected?", I would just check if the wiring is good (wires well inserted on the pins), or I check if the soldering is well done.