Two years to say goodbye, and make sure all his affairs are in order. I bet he made that decision the day Severus died. "I can last two years to see the last grandchild graduate from Hogwarts, and gift all of our accumulated possessions so there will be no bitterness among the children over a will, but that's it. Two years." And now, sweet relief. He stuck by his resolution, and can now rejoin his love forever.