@Jan45
Apps can either use their own (local/internal) CC/subtitle settings, or they can use the Roku system's global/external CC/subtitle settings.
Apparently the app(s) you are using use system/global/external CC/Subtitle settings, such that if the CC/subtitles are turned off in the app, they get turned off globally (in the system settings, for all apps).
There are also numerous bugs in the firmware/various apps that handle CC/Subtitles that can also cause such behavior, in addition to Roku's poor CC/Subtitle functionality design.
The best you can do is make sure Settings/Accessibility/Captions mode = On always and be wary of turning CC/Subtitles off within an app (try to turn them on in all apps you use) because that may turn off your system/global CC/subtitles settings.
Otherwise, you should contact the app vendor directly via the help/CS and request that they use local/internal subtitles (and not the system/global/external subtitles) as well as Roku and suggest they fix/change their subtitle functionality.
NOTE: Apps/services that use internal/local (their own) subtitles and subtitle settings have to be configured independently per app, and changes made there do not affect the Roku's global settings, and vice versa.