Try refreshing the page
The problem manifests itself when I revisit the analysis after closing the analysis report session. So refresh won't have any effect as the saved version is what is being displayed - minus the "Comment Before". edit.
@jas0501 thanks for reporting this. Can you please doublecheck if its still happening? I tried everything and i cannot get it not to save my comments.
Still occurs for me, Here are the steps to reproduce it.
1. go to the archive and select a game for Analysis
2. From the analysis tab pick a white move that is less than the best.
3. Click the magnifying glass to inset the best move sub-line.
4. Select Self Analysis
5. For the sub-line just inserted inset a Comment Before on the first move of the sub-line This is a test before, so the comment is inserted right after the parenthesis.
6. Insert a Comment After after the last move of the sub-line This is a test after.
7. Save
8. exit the analysis.
9. go to the archive and revisit the analysis
10. The comment before is missing
I think the key aspect is the lost comment is a Comment Before on the first move of a sub-line.
Just tested level 2 sub-line Comment Before like so (^....................(^.........................).................), inseting at the ^'s, after the parenthesis and it too is lost. So it appears the bug is leading comments on sub-lines get lost. Not just level 1 sub-lines.
I followed your steps exactly but the comments all seemed to save 
Can you perhaps try to catch it on video?
My clumsy attempt as video capture is here:
https://www.screencast.com/t/ehWUhhzNZA
The transition back to the saved analysis could be better but you get the idea. Note you have to look quick at the end, or pause, to appreciate the missing comment.
Here are screenshots, note the times at the bottom:
Bug: Comment Before edits at the start of a sub-line are not retained after saving.
In my first foray into experimenting with the Self Analysis edit feature I encountered a bug. After adding a Comment Before in a sub-line starting with move 12:
and saving the analysis the comment is missing upon revisiting the analysis
It may be the comment is saved but the redisplay gets tripped up, or it just gets lost.