In Gmail the most crucial issue is, if someone not able to send and receive the messages to anyone. Behind this issue several reasons are here which prevents you to send and receive the mail. But if you want exact solution regarding this problem just go with below points where I mention some important steps to overcome of this problem.
1) If user successfully sends the mail but same time he founds that its message has rejected. The mail rejection means something happens wrong in your message. Kindly check the common mistakes in your mail such as: spelling errors, quotation marks error, if there are dots at the end of address or extra spaces between the address then definitely you have to suffer this issue.
2) Some users send the mails but their recipients didn’t get that mail it means your message getting delayed. In this situation, first of all you should know how people sending the messages means how they send the messages like: through mobile device, outlook or apple etc. Simply check the configuration and setting of your Gmail account in your mobile device.
3) If users IP address has changed then you will receive an error message and didn’t send any kind of mail or receive mail. Try to use other internet connection. Or you can contact to internet service provider or network administrator to solve this issue.
4) Due to the failure of authentication users are not able to send or receive mail because your email server cannot verify your email access is authorized. It happens due to mis typed password or wrong password. So reset your password immediately and confirm about your username and server name.
5) Have you checked your web browser because due to browser problem it happens. The most supported browser for any web mail services are: Google chrome, internet explorer, Mozilla Firefox etc. If you using these browsers then surely you send and receive the mails.
You have another one option if the above steps are not suitable for you, immediately contact to Gmail technical support. They provides you best support regarding Gmail and step by step they resolve your problem.