ESP8266 and Arduino - SoftwareSerial vs Serial problem
This is the info taken from arduino website:

The library has the following known limitations:

1) If using multiple software serial ports, only one can receive data at a time.

2) Not all pins on the Leonardo and Micro support change interrupts, so only the following can be used for RX: 8, 9, 10, 11, 14 (MISO), 15 (SCK), 16 (MOSI).

This has not explicitly mentioned the board you are using, but I think these limitations are on hardware level. Changing the software serial pins should most likely take care of this issue.