Simple:Press does not send out emails. It is WordPress that sends all of the emails. So the first thing you need to determine is – are ANY emails being sent. I.e., emails to new registrants, password changes etc…
If they are not then it would be a server/hosting issue. But – WordPress is notorious for being a little flaky on email sending which explains why there are some good SMTP plugins about We actually have to use one on this site to resolve this same problem. The one we use is called ‘HGK SMTP’ and you can find that and others in the WP plugin repository.
If you determine that only SP derived emails are not being sent then do check the forum admin > options > email settings to ensure those values are correct. These simply alter the ‘send’ data for standard WP emails which usually show as coming from a user called ‘WordPress’ – something most users do not, understandably, like,