A window install like that requires careful attention to flashing. The mortar is not intended to prevent moisture infiltration, that would be the job of the flashing. When I put my French doors in, the manufacturer presented very detailed instruction regarding proper flashing, which involved a combination of ice and water shield, felt, and metal flashing, in multiple layers. Based on experience examining failed window installation, I would say that improper flashing is a common cause of trouble, since to do it right is time consuming, and a low bid installer may be tempted to cut corners.
Wind driven rain penetrating around the window is a pretty common sign of failed flashing, and unfortunately there is no way to fix it that I am aware of short of removing the stone, installing proper flashing, then reinstalling stone.