Can you access your server with SSH?
I was just thinking, someone who's literate would not be asking about issues as vague as this. But we can fix that! SSH is short for Secure Shell. It's the preferred method for administrating UNIX machines (Linux, Mac OS X, etc). It provides you with command line access to a machine over a network. But I don't think we need to go down that route yet. First, can we get any specific numbers from GoDaddy? I couldn't find what the specs are for "Level 2" from a quick browse of GoDaddy's website (but I didn't look all that hard, because I don't wanna be on GoDaddy's website). Can you link me to a list of them, and you can provide numbers for how much your site is using of each resource, and, even more useful, can you provide numbers about the rate of usage of these resources? I'm thinking if your site is small, and WordPress based, it's probable that your website has been hacked and is exploited to send out spam email or capture sensitive visitor information. High resource usage contrasted with low site visitor counts is evidence for this. The other thing you can do, if you haven't already, is install the free Sucuri Scanner plugin for WordPress. It will help you harden your websites against attack and determine if you have been hacked, and, if you have, help you recover.
Ok, so here are my resources and where I'm at right now. It doesn't seem to be a consistent problem, apparently CPU Usage and Memory Usage is spiking sometimes, which triggers the warnings. I am running 7 Wordpress sites on that, with a combined 4,200 hits per month (that's what the GoDaddy rep said). Which seems like very little. I talked to GoDaddy, the dude had me click on some PHP optimization options and compression, but said Wordpress has become very resource intensive and I should consider upgrading (that sounded like a sales pitch for the sake of it). I will now check out the Sucuri Scanner plugin, thank you!
Here are the stats for the 7 sites: http://imgur.com/a/FmSPp Mhmmm, according to those stats I guess the 4,200 hits were daily. Edit: Ok, I just realized I'm getting a ton of referral spam... can that be an issue? Now on to blocking it.
I administrate WordPress sites on shared hosting that, on average, use 20 plugins, and I have no significant performance issues. But then I also run the shared hosting, so I can allocate resources as I please. It is possible, however, for larger numbers of plugins to cause performance issues. Some plugins, especially ones that aren't as mature, popular, or stable, may not place nicely with each other, and it's true that bugs in one module could potentially slow down the whole site.