My background is 35+ years writing programs for main frame computers, so I have seen it all when it comes to something suddenly not working. Like others who have this problem, the subtitles were working fine the last time I needed them. Let me warn you....the solution is not something you would expect.
I tested it on two movies. Both were >MP4 format. The movies are on a USB drive. The .srt files are saved in the same folder as the video, and have the same name as the video. And yes, I went to Settings > Accessibility > Captions mode on my Roku TV and verified that the "Captions mode" was set to "On always."
You can tell you have a problem by starting the movie, pressing the asterisk (*) button and selecting "Accessibility". Here you can verify that the "Captions mode" is set to "On always." However, if you look at "Captioning track" directly beneath it, it will show "not available." This indicates the .srt file is not being recognized.
Both movies were sequels. As a result, both names had the number "2" in the title. Someone before me (...only one person) suggested removing all numbers from the name. Stupid I know, but it worked. I tested two (...no pun intended) different ways.
For the first movie, I simply removed the number "2" from the movie and .srt names. For the other, I changed the number "2" to the word "Two". In each case the movies played with subtitles. To see what this changed, press the asterisk (*) button and select "Accessibility". Again you will see that "Captions mode" is still set to "On always." However, if you look at "Captioning track" directly beneath it, it will now show "Single track." This indicates the .srt file is recognized.
That's what worked for me. See if it applies in your case.