OK, we tried different options and it looks as follows:
Unfortunately, the subtitles also disappear on a recorded program (it’s just the way it’s defined by the provider of subtitles). But there is a work-around: You may record a program, play it and when you feel to re-read the subtitles, you may wind back and then replay the respective scene. Might not be the most fun way to do it but at least one option.
Hope this helps.
Wishing you a nice evening!