The subtitles first of all are too much to the right. I am not sure if this is how they are supposed to be, but I don't think it makes any sense and I've never seen this done before, the lines first letter is almost at the center part of the screen at the bottom.
Considering this is a 16:9 (4:3 picture w/ pillarboxing) Blu-ray, with a 4:3 cropped re-encode, the problem is that [a-s] muxed the full-frame 1920x1080 PGS as-is. VSFilter only contains a method for vertical padding, which won't help you at all since you need horizontal padding.
How to fix 1920x1080 PGS on 1440x1080 video:
Option A) Demux the PGS subtitles, use BDSup2Sub
Convert Resolution to 1440x1080 & Free Scale Y=0.75, export/save them as SUP(BD), and mux them back into the MKV replacing the existing PGS subtitles.
Option B) Use FFDShow's resize filter to re-add the black pillarboxes on each side, "Specify Aspect Ratio = 16:9" & "Keep Original Aspect Ratio"
Option C) Use MPC-HC's internal subtitle renderer for watching shows with cropped video and PGS subtitles
Option D) OCR the PGS to ASS softsubs (hint: [a-s] has two different FMP BD releases, one with PGS and the other with ASS subs)
Note: For all of these options, leave xy-VSFilter vertical padding set to the default setting of "Original height".
And now I also get why the vertical padding didn't work : I had set it to extend 16:9 instead of crop 16:9 (but why in hell does it say extend to 16:9 in the guide then lol).
Setting Vertical Padding to 'Extend to 16:9' is only correct for vertically cropped 16:9 video with PGS subtitles. Vertical Padding
shouldn't be used at all for horizontally cropped
video. Setting 'Crop to 16:9' will just crop off the top and bottom of your 1440x1080 4:3 frame to a 1440x812 16:9 frame, which probably isn't what you want. If you have a 16:9 monitor, watching a 4:3 video like this one isn't supposed to fill the entire screen. Having black pillarboxes on the left and right sides is normal.
The bigger problem is that they keep disappearing, especially at around episode 9 and 10 for a few lines here and there, which is annoying even though I for the most part understand what they're talking about. Is this a problem with the file itself? I don't know what it could be. I tried messing around with the subtitle buffer but to no effect. It might be that because the subtitles are too far to the right and when a longer sentence comes it is cut off completely?
If the issue is 1920x1080 PGS on 1440x1080, you are correct that subtitles which exceed the 1440 width of the video frame which VSFilter renders to, wouldn't be displayed.
If instead this is an issue with multiple overlapping PGS lines not being displayed, this was a known issue in VSFilter's PGS parser for years, which just recently got fixed by MPC-HC a month or so ago. The fix for multiple overlapping PGS has already been merged into xy-VSFilter, and will be included in the next stable release.