I tried to click in the "click here if the download does not start" link, but that did not make the subtitles being downloaded.
In the picture
Func posted above of the subtitles page, can you see the
.srt file name there:
"Parasite (2019) Bluray-1080p.pt-BR.srt"?
If so, forget the download button and all the other ways of downloading a subtitle, and click on that link itself. That should download the subtitle straight to your downloads folder even without a zip folder. So just the .srt file.
Make sure you're not over excessively using cookies block and strong privacy settings on your browser that may cause some websites to break. The above is a fool proof method that has always worked, no matter what happens to the website. Try to download that way. Last but not least, also try it with a different browser.
Don't think you're experiencing a major issue that's affecting a lot of people, but an issue nonetheless. Will be put on the fix list.
Cheers