I think your mysql server went down due to high load (or there might be another issue as well) But you can rectify this by doing some optimizations (if you don't want to upgrade to vps)
For example there are many plugins for cPanel varnish, nginx that can increase your website performance which will reduce mysql errors then. Varnish and nginx are both easy to install.
Plus you can apply cloud flare to your website, cloud flare will also reduce the load on your site.