Though the plugin successfully sends millions of emails every day, there are a host of issues that can stop or delay emails on both the sending and receiving ends. It depends entirely on your local Server & WordPress configuration. You will need to investigate this issue for your particular local configuration.
See Contact Form 7 Email Issues. Most people that work through this information appear to be able to resolve their email sending & receiving issues.
In your case, make sure you look at Using the default From: [your-name] [your-email] can cause problems.
I had this working well and all of sudden emails are not being sent, even though it says it was sent successfully. I disabled all of the plugins to isolate if one of them was causing the issue. It did not resolve the problem. I saw posts from a couple of years ago with this same issue but I can’t get their solutions to work. Can someone please help me? We are probably losing important email messages.
Thanks!
The plugin is working before but few couple days it is not working when I change email address .I need to solve it .please help
RE: it is not working when I change email address
There is a link at the bottom of the page Contact Form 7 Email Issues (that I recommended to you) to a comprehensive and detailed article which covers your issue.
I wrote the article specifically to help the people, like yourself, that have trouble sending emails from Contact Form 7.
You may need to work through each of the steps recommended in that article to solve the actual problem for your particular local configuration.