If you have a large forum and are running into issues sending too many emails to your members, resulting in the script being disabled by our automated systems, or you are on a dedicated server and your script is crashing your server, you can set up a rate throttle so that you are in line with our shared server email policy, or to prevent your dedicated server from crashing.

This requires a plugin to your vBulletin software. As of this writing, a suitable option has been located to help you accomplish this task which is located here:

Cron based e-mail sending - vBulletin.org Forum

You might want to check with vBulletin support to see if the current version supports email rate throttling as new releases are constantly coming out and new features are always being introduced. It may be possible to rate throttle without adding any mods at all based on what their support tells you.