Is it a good idea to keep in touch with your ex?

I broke up with my girlfriend a few months ago and I told her I'd still be by her side whenever she'll need me, but lately it feels like she's taking it for granted. Coincidentally it's the main reason why I broke up with her.

She keeps doing subtle jabs at my faults in the relationship out of the blue when we're talking, which is mostly me comforting her, so it's starting to get extremely annoying.

Are there any benefits to keeping in touch with your ex?