then maybe there is something I have to do on website and i didn't done ?? what do you think ??
I think you should check your SMTP provider mail configuration. See above post with link
Then enter that info to AbanteCart Mail settings page. Make sure you type it...not copy paste coz you simply can copy space or some other chars.
If do not work after that check the Error log on your server (and another error log in AbanteCart, your servers log is more important)
If that also do not help. Set up Gmail SMTP to just try out is it works at all.