how to turn off subtitles so they stay off

Verify the Closed Captions and SDH setting in:

Settings﹥Accessibility﹥Subtitles and Captioning﹥Closed Captions and SDH﹥On|Off

That setting would apply to each new video, regardless of the last change during playback.

It may have been enabled accidentally using the Accessibility Shortcut (triple-click Menu/​Back).

I'd actually like to have the closed caption/subtitles on for some of my Audible books and I can't find where to turn this on. They were there one moment and I must have touched something and suddenly subtitles/closed caption was off. I do not see any setting in Accessibility to turn this feature on. Also what is "SDH"?

… for Audible books

My previous reply was for video content. Audible books may be different and independent. I think Audible tried to include that, but then were threatened with lawsuits by publishers, as their original contract didn’t cover such use. iOS has options for Live Captions, which is perhaps useable with Audible?

Also what is "SDH"?

Again for video content: SDH stands for Subtitles for the Deaf and Hard of hearing. It has more descriptive words than just the dialog subtitles, i.e. [loud bang], [sad music playing].