"You're missing the posts only available to members" — should there be a "the" in there?

Although the modifier "only available to members" makes "posts" more specific and thus would seem to require the definite Article, it still hasn't made the Noun completely specific.

You can say "posts" is halfway from being general to being specific.

This is often confusing. Consider this other "middle" example. This is correct:

Ex. I like people who have initiative. (not all people, but still general)

In your example, not adding an article is suitable because the Noun "posts" is specific but still general.

The alternative you're thinking of should be something like:

Ex. I want to read THE posts that WERE only available to members.

The problem is not with the article, but with the compression engendered by reducing the relative clause which/that are available to members by Whiz-Deletion. Put the boldfaced material back in and it doesn't matter whether you use an article or not. The following are both grammatical and semantically identical

• You're missing posts that are only available to members.
• You're missing the posts that are only available to members.

The only difference is whether you want to go on record, in the second example, as assuming that there are posts that are available only to members, and as assuming that your listener already knows this. Or whether, in the first, you merely want to imply their existence and allow your listener to form their own conclusions.

Because that's what the does -- it marks presupposed existence in what is called a "definite description" in philosophy and linguistics. How definite you want to get is up to you, and depends on your audience. This isn't a correctness matter, but a presentation matter.

Posts available only to members makes a generic reference, that is, a reference to a whole class rather than to specific instances of the class. As explained in the ‘Longman Student Grammar of Spoken and Written English’, this can be achieved by use of the definite article, the indefinite article or the ‘zero’ article. The indefinite article clearly isn’t appropriate here, given that posts is plural. The definite article is used generically only with singular countable nouns. The ‘zero’ article is used generically with plural and uncountable nouns and is what you require here, as in your first example.

Omitting the from posts makes it a general reference. What you are saying is that posts in general are available only to members. If you want to refer to a specific set of posts, you need to add the. But in this scenario the meaning is clear whether you add one or not.