I don’t see anything in what you provided that would cause the post not to update. From the look of it you are including the form on the same post that the content is associated with, that is the single php template for the post type, whatever that is.
If this is not the case and you are showing this form on some other post or page on the site then you need to provide the correct post_id argument when calling acf_form().
If that’s not a problem then maybe you’re seeing some kind of a caching issue. Do you have a cache plugin running on the site?
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