Problem with trafic

There are problems with the site on Wordpress. It is added to google news. Periodically receives a sharp increase in traffic when news gets into the Google API. Since the site is located on a shared hosting, shutdowns started due to server overload. We connected http://cloudflare.com, installed the plug-in and the load decreased significantly, but when cloudflare is activated, traffic with the Google API sharply decreases after 30-40 minutes (from 200-300 people online to 50-80) and from the usual 30,000-40000 visitors per day 4 consecutive days we received no more than 10 visitors per day http://prntscr.com/q5fnj3. I put the cloud on pause and the next day received a sharp jump of up to 38 to visitors. Can you help me figure it out?