Simple to reproduce: (note: only non moderator 3K+ users can reproduce)
- Go to a question.
- Cast a close vote as off topic choose Other and put custom comment. Confirm.
- The custom comment is added and the "add comment" link disappears.
After refresh the link appears as usual.
For what it's worth, Chrome 28.0.1500.72 here but I'm 99.999% sure it's not related to browser.
Sometimes there is no "add comment" link at all even after many reloads. When it happens I noticed additional request to the server which doesn't appear when the link is present: https://meta.stackoverflow.com/posts/190301/comments so this leads me to believe that on certain condition which I can't reproduce, the whole comments placeholder is replaced with the result of that request, and indeed there's no "add comment" link there.
Didn't happen, guess that one was fixed.