I have 2 wordpress sites on a DO 5$ instance. I had 1-10 visitors a day on the sites and had no problems.
The setup is nginx +php5-fpm + w3 super cache + cloudflare
I starter getting about 300 visitors a day for one site and i have noticed the site sometimes was showing blank pages.
I was also getting timeout from cloudflare, and the site was moving very slow. Tried to disable the cache plugin but it was the same.
I have upgraded to the 10$ instance, and still could barely navigate in the wp admin area..
This took 2-3 days, now the site looks to be ok (traffic has dropped to 150 day), i think it was a memory issue with their server..
Also if i do a : ab -n 500 -c 200 http://site.com from another server my site stops working..