Why links are not linked if edited comment?

The plugin author has solved the issue. He says:

I have encountered this bug before, but I just now realized what’s
causing it: the ‘comment_text’ filter is not applied on the updated
comment content. The make_clickable() function, which makes the links
in the content clickable, is hooked to this ‘comment_text’ filter.

Anyway, it’s fixed now:
https://github.com/scribu/wp-front-end-editor/commit/e590a39522c89ca8016e52f7dcc26d33d552e69c

You can try out that fix by downloading the Development Version
(2.3.2-alpha).