If you aren’t using dedicated server or VPS, your host is probably having limit on number of emails that your account can send in some period.
You should see this in your host’s documentation or support to find this out. For example, SiteGround for its StartUp and GrowBig WordPress hosting plans is having a limit of 400 emails sent per hour. You can see other limits on MailPoet site.
Most sites don’t reach this limit, but there are cases where sites send large number of emails and require more resources than available. Other, even those that don’t have limits, send large number of emails at once and create heavy load on server.
Because of this, I have created solution for WordPress that allows you to behave according to limits while still sending all emails you want.
Simple Email Queue is a free plugin for WordPress aimed to developers who can set limits by using of filters and then using dedicated function (that is alias of built-in wp_mail()) for sending emails.
Simple Email Queue Plus is a premium plugin aimed to all users that provides user interface for free plugin and additionally reroutes all emails sent using built-in wp_mail() so that it passes restrictions.
Both plugins are very light, try to add minimal footprint to your WordPress installation and use minimal resources and database options.