I'm seeing the same issue on a few Studio videos and I have an open ticket with Instructure support. Were you able to find an answer or solution?
This is what we observed:
When attempting to download the SRT caption files in Firefox, the browser opens a new blank tab rather than the save file pop-up. When attempting to download the SRT caption files in Chrome, it returns a "site wasn't available" error.
My team was on a deadline and needed to move fast, so our workaround was to download each video file, reupload to Studio, and correct the captions again. The caption file download worked as expected on the newly uploaded version of each video. It is not an ideal solution, but I'm sharing in case it helps.