What speed are you prinint at? The Y-axis stepper needs to pull the weight of the build table to and fro. It may be that the Y-axis stepper motor is skipping steps when it (or the electronics) get warm.

You can check this by reducing the printing speed by at least half and trying to print again. If the print then goes well, you can try to increase the current to the stepper by adjusting the pot on the stepper board. Turn it a little clock-wise to increase tha max current. Also check all cables and the soldering of the connector on the main board.

It may also be that you have found the mechanical upper limit of what your Y-axis can handle.