This is unlikely to be a theme issue and it is most likely server or plugin related. 

To test this, activate the default Twenty Twenty-One theme (don't worry this won't affect your site content). If the issues still occur this means the theme is not causing the issue. Make sure whatever plugin you're using is set up correctly and that you have no typos in your email address.

If your server does not allow emails to be sent out try using the following plugin: 

https://en-gb.wordpress.org/plugins/wp-mail-smtp/

For BuddyPress emails you will also need to add the following to your functions.php file:

add_filter( 'bp_email_use_wp_mail', '__return_true' );