Once Anna sleeps with Vronsky, there's the narrator tells us that she feels that she has committed a terrible crime, and Vronsky feels that he is looking at a corpse (Anna) whom he has murdered. This is the first sign we get that to commit adultery is to be thrown out of the social world. Anna may not be literally dead, but she is socially dead. Even though Petersburg society is relatively liberal, they aren't going to let a woman get away with living with a man who is not her husband. And once Anna's friends – even the notoriously immoral Betsy Tverskoy – stop seeing her, Anna is left entirely dependent on Vronsky. Her social isolation ramps up Anna's guilt (over abandoning her son), jealousy, and paranoia (if Vronsky leaves her, she'll have nothing left).
Levin, on the other hand, has trouble connecting socially because of his general existential angst. Anna is good socially, at first, even though she's eventually isolated from social circles. Levin, however, is bad socially, at first – he's always getting into intellectual fights – and has to learn how to interact with people less antagonistically. It's only upon his marriage to Kitty that Levin stops grandstanding all the time and starts listening more humbly to his friends.
Anna kills herself because she believes that she is utterly alone without Vronsky.
Levin's decision not to tell his wife about his spiritual epiphany is a good one – it does not signal any failure in their relationship.