The Leonardo has two hardware serial ports - Serial that uses the USB-to-serial converter and Serial1 that uses pins 0 and 1. Why are you using SoftwareSerial?
I'm sure that somewhere there is a list of pins that support pin change interrupts, which SoftwareSerial needs, but I can't find it. On the Duemilanove, all pins support pin change interrupts. On the Micro, which uses the same chip as the Leonardo, not all pins do. On the Mega, not all pins do. The key is which ones don't.
If you MUST use SoftwareSerial, you MUST determine which pins support pin change interrupts, and use only those pins.