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“Every time you’re with another woman, you abandon you,” Vanzant told Maxiell on the episode that aired last week. “And every time you tell another lie, you abandon you. And every time you take a drink to stuff the pain down, you abandon you. This wasn’t about sex. This was about punishment.”

I'm not sure what "you abandon you" means in this context. The close definition in the dictionary for abandon I got is:

4. verb
   If you abandon yourself to an emotion, you think about it a lot and feel it strongly, especially when other people might think you are wrong to do so.

But I'm still not clear how it can fit for the context.

What does it truly mean here?

The full source.

"You" is used here instead of "yourself", possibly to sound better or more memorable. This is a common usage in the language of therapy, self-help etc. Vanzant says that every time Maxiell sleeps with another woman, or tells a lie, or drinks to dull a pain, he is abandoning himself (ceasing to care for himself responsibly).

The article you linked to says that Iyanla Vanzant is the presenter of a self-help TV show called "Fix My Life". Her remarks should be interpreted with that fact in mind. She is saying that when Maxiell e.g. sleeps with another in a series of women, he is not doing so primarily because of sexual desire, but rather because he is stuck in a pattern of self-destructive (self-punishing) behaviour. When he gets drunk it is not because of his great love of fine wine or whatever, it is also because of that.

you abandon you as Michael Harvey rightly points out in his answer is a cant phrase from the therapy / self-help domain; the second "you" there is the true self you need to nurture. And the verb abandon is not to be understood in the sense lose all inhibitions:

They abandoned themselves on the dance floor.

Rather, abandon there means something like "leave behind and forget all about":

He abandoned his wife and family and ran off to join the circus.

you abandon you is not a reflexive construction. The second you is a reference to "the self" and is not to be understood as the reflexive pronoun "yourself". This is how that phrase could be typeset:

...you abandon "you" ...

In "olden times" (before the 1980s) much the same sentiment might have been expressed as you are not being true to yourself.