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.