If you can narrow down exactly what & when it happens to have a better idea of the circumstances then you maybe able to duplicate those circumstances in a quick timely manner. If not, you may have no real choice. Your options maybe in that case to either shut the plugins off for a few days and just post an apology to members letting them know you are trying to fix a site problem or hire a programmer to find the problem for you. Which I really don't know that they would be able to take too many other steps avoiding turning off the plugin system globally but I'm not a programmer yet so I do not know all the possibilities for that particular instance. You may want to do a few things to see if you can find any errors first, but I really personally think this is related to a mod you have installed, it almost always is. But do the following first:

1. Check your server logs to see if there are any PHP errors or MySQL errors on your server. If you do not know where they are ask your host they should be able to help you.

2. Check all your email settings in your cPanel. Plesk WHM or whatever you run on your hosting account to ensure they are correct.

3. Ask your host if they have made any changes since this has begun. Who knows they may have updated something that caused it to go nuts on you.

If you come up with nothing after those then your only other option is shutting off the plugins.

That could be an option, but the only problem is to duplicate the situation the site would have to be live and sending out emails. A test server is not likely to do that and you cannot run two live instances of vBulletin on one domain without having two licenses. So that really may not be an viable option.