Post Date Wrong – 1 Jan 1970

I have custom post, post and pages. I created them manually. I modify manually. Sometimes I also use CSV import to update.
The dates of the custom post and pages etc seems to always changed to 1 Jan 1970 whenever I modify a custom post, page etc, regardless of the method I modify it (i.e. manually by editing the post or by importing changes using CSV import).
I set my date in General settings to Month / Day / Year (eg March 23, 2014).
I am not showing the date for custom post and page on my website as it is live and the out-dated dates is simply not going to give a good impression.
Please advise.