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He lives on autopilot.
Every day, just going on for the sake of it. He's not sure what for the sake of. He has no reason to live.
He hates himself for all of it, the things he could have said and didn't, the things he should have done and never did, the people he should have stood up to and the person he should have been.
He has one reason to live, though. The boy. The boy who has all of his father's arrogance, but if you look closely, is more like his mother than anyone gives him credit for. If Snape hears that Harry Potter looks exactly like his father one more time, he'll scream. Other people don't see it, the forehead, the nose that's slightly more streamlined than James's was. Her forehead. Her nose. He brings these things up in passing, muttering "He doesn't look exactly like him" when he hears Slughorn talking about Harry to Dumbledore. Slughorn doesn't hear, and Dumbledore pretends to go temporarily deaf, twiddling his thumbs and looking at the ceiling.
Sometimes he considers performing Legilimency on Harry in his sleep, just to see Lily's face one more time. He quickly shoos the thought away, though. That would shatter the careful facade he had managed to put up.
Severus Snape lives on autopilot.
Which is why only when he is dying, does he allow himself to let down his guard, and truly look into the face of Lily Evans through her son.
He doesn't believe in heaven. Or hell. He's not sure where we go on to. He just hopes Lily's there when he gets there.