I have experienced the same problem for the past 3 months. At times much worst then others. I have spent the past 2 days on phone with support and this is their conclusion:
A few months ago they made 'modsecurity' changes to their servers to help prevent against bruteforce wordpress attacks. Well in making these changes they screwed many of us over by limiting the amount of post requests your site or IP can make at a given time -(the post requests can be theme related or plugin related as well which is why not EVERYONE with a wordpress site has these problems).If too many requests are sent, the site will crash out for a limited time. Now here's the kicker, the only given fix is to upgrade to a dedicated server, costing you a ton more money, or you can run a VPN under your current, which is ridiculous to have to do. Keep in mind that they made these mod_sec changes without notifying any of us they were dong so, and people are still losing their minds trying to figure out the problem with their site.
The only REAL conclusion is to move hosting companies. Shame on you Godaddy.