What is happening when I create a post with quoted text, and it shows up in preview, but when I post it disappears?
It doesn’t happen every time, but a lot.
If the post you’re replying to is immediately before yours, Discourse takes it upon itself to not clutter the thread with “unnecessary” quoting.
I always add a dash, look at your (quoted) post to see what I mean.
Editing the quoted post will preserve it.
If you quote the entirety of a previous post without any changes, this happens.
I add a period or delete a period to the quoted text, or change it in some way and it works.
ETA: yeah, what running coach so eloquently stated mere seconds before me. 
Thank you all.
So the system knows what is best for me. 
Just like Windows.
More accurately, just like a lot of other soi-disant features of Discourse. It follows the arbitrary preferences of its developers (like most software) but it’s also amazingly rigid about imposing those biases. In a sane world, this particular pathological behavior could be configured off by admins, but I don’t believe it can be on this platform (judging by the ubiquity of this behavior on other Discourses I’ve used).