You don't really want auto purging. The problem here is that the nginx cache size is set larger than the available space. If you check /etc/nginx/conf.d/fastcgi.conf you'll see max_size=256M (which is WordOps default and not scaled by server size). Given that tmpfs/run is 197MB you probably have 2GB of server memory. So try reducing max_size down to say 120M (the server needs some of that 197M). That way nginx can more efficiently manage it's cache.
You can get an idea of cache efficiency by getting counts of cache hit/miss from the log files:
sudo awk '{print $3}' /var/log/nginx/yoursite.com.access.log | grep -E 'HIT|MISS' | sort | uniq -c
If you get a percentage hit from before and after changing max_size you'll have an idea if it's working better.
That may not fully solve your problem as caching is very dependent on type/use of site. You may need to move cache to disk rather than memory and give it more space to get things working efficiently. Or you may need to do more to stop bots hammering your site.
Oh, and also make sure you haven't turned on preload mode in the Nginx plugin. Fine for sites with small numbers of pages but will totally break caching for large sites and low memory space.