Q:

should comment be deleted silently with no notify of the reason?

I see many of my comments are deleted without any notification and mentioning the reason to I can re-post them corrected. 
This is not fair action. 

A:

Comments, by design, are ephemeral; not only are they easier to delete than a full-fledged post, but also much more impossible to recover. The Comment Everywhere page, provided to all new users when they earn the privilege to comment, describes them as "temporary "Post-It" notes."  And in a Meta.StackOverflow discussion on exactly this topic, Jeff Atwood (one of the founders of the Stack Exchange network) explicitly describes comments as "third-class citizens". 
Even without moderator intervention, any comment may be permanently and silently deleted just by accumulating enough flags, flags which can be cast by regular users.  Some comments are even easier to delete than others.
As a moderator, I'll occasionally go through comments and purge the ones that do not provide value to the actual post (i.e., the Question or the Answer) itself.  In particular, any comments which fly against the guidelines provided in Comment Everywhere may be struck without warning.
This sort of clean-up is important to ensure that the meat of the site, the Questions and the Answers themselves, are not drowned out in noise.  If I feel it necessary or valuable to do so, I'll leave a comment explaining my actions, but when the intent is to eliminate noise, adding more comments is counter-productive; especially if I feel such comments are likely to solicit replies.
If a comment does provide permanent lasting value, it is often if not always better to flesh it out into an answer in its own right, or to edit the information into an existing post.  Actual Questions and Answers actually have recourse against deletion (be it warranted, accidental, or malicious), as any deleted post can still be edited and un-deleted; comments have no such protection.

