Why is my print displacing along the y-axis by 2-3 cm?
This has happened to me in the past and here are a few things that I determined could have been the cause:


Limit Switch triggered. My coworker was able to repeat the issue by manually triggering a limit switch during the print. Somehow, this seemed to cause the relative axis to shift on his MakerBot Replicator 2.
Skipped steps. It's possible that, if stalled due to excessive load, the stepper motor could skip steps. I have a dual extruder, so if a part curls really bad then the second nozzle gets caught in the print. I'm not sure exactly how this works, but my coworker suggested this as an issue.
USB connection. I had sliced a model and tried printing over USB connection, however each time I attempted the print I encountered the "shift" at the same exact location. However, using the slice, I exported a G-Code file and printed from the machines SD card with no errors.
Slicing Engine bug. This is in correlation to the USB connection issue. I noticed that the issue occurred after updating my slicing engine. My solution in the long term was to re-install the previous version that was stable for me. I was using MakerWare 2.4.2 and reverted back to MakerWare 2.4.1.


If you're printing via USB connection, I'd suggest exporting to G-Code if you're able to print via SD Card until you can find a stable version of software for your machine. This has been the most repeatable solution for me in the past.