I recommend asking at https://wordpress.org/support/plugin/wp-mail-smtp#new-post so the plugin’s / theme’s developers and support community can help you with this.
Do you mean “not sending” in the literal sense or do you actually mean “not getting to my user’s email inbox”.
There are ways to track SMTP usage through logs, it will depend on what you are using, but if for example, you are using sendmail, you can check out this tutorial: https://serverfault.com/questions/59602/where-to-check-log-of-sendmail
If you find out that the emails are going out, I’d look into the issue of spam/whitelisting. Your emails might be getting there, but they could be in the SPAM folder. I’ve enountered this before and the workaround I found was to use a transactional email service like Mandrill (from MailChimp) https://www.mandrill.com. It’s neat because the service has a WordPress plugin https://wordpress.org/plugins/wpmandrill/ that you can set up really easy and it automatically overrides any WP MAIL or any email server related stuff. You won’t depend on SMTP anymore.
Hope this helps guide you in some way.
