Due to the way MCEBuddy processes the files you need to extract them and then put them back in. So, you have to Enable “Extract subtitles and closed captions” under subtitles. This creates a SRT file. And if you leave it like that the srt file will follow to the final conversion location and most players recognize that there is an srt file and will enable playback with the subtitles. But if you want to re-embed the subtitles you’ll need to go to Expert Settings and enable “Add subtitles” under the Subtitles and Chapters section.
It is a little confusing but when MCEBuddy starts a conversion is creates a working copy of the video file which strips out subtitles and chapters. Basically leaving only the video and audio tracks. This is the step labeled “Remux to MPEGTS or Copy source file to temp” in the process MCEBuddy - Conversion Process Overview