Ouch. Maybe it's a bug in AltSoftSerial?
Could you try sending the data from a PC to AltSoftSerial's receive pin at 57600, with the sketch sending it back to the serial monitor at 115200?
If that also shows the problem, could you please send me the exact code and specific details of the hardware, operating system, software versions and everything else you're using, so I can try to set up the same system here and see if I can reproduce the problem?