I would renew the subscription since that covers both software updates and support from Appnitro;- this forum is not the official source of technical support.
Your emails not sending would not be caused by your subscription expiring (coincidence....)
Check the email details in the Machform settings. I would suspect it may be an issue with the email service provider - whether your host, ISP or Gmail or whatever. Check what method of email send you're using e.g. SMTP or PHPMail etc.
We can't see the back-end of your hosting to check all that stuff, but Appnitro could have done, if you could lodge a support ticket, that's the sort of thing they would ask you for to enable them to check it.