It could be to not enough RAM available. If your service ran out of memory, it’ll get killed and you can have problem like above.

You can look for logs. Start with syslog:

nano /var/log/syslog

Look there for entries like OOM, OOM killer, proccess killed, out of memory. If you find that logs, it means that you don’t have enough RAM.

If you can’t find logs there, you can also look for alternative location /var/log/messages.

In case this is the problem upgrading Droplet or installing Swap would do the job.
How To Add Swap on CentOS 7 or for CentOS 6 How To Add Swap on CentOS 6.

I had the same issue a while back, and yes, it was the RAM running out taking down MySQL with it. Increasing the RAM size and adding swap fixed that for me. Swap though degrades SSD drives so opt for an increase in RAM if you have the budget for it but swap will do if you’re tight on cash.

Back then, I used New Relic to monitor my servers that helped me identify the issue. You might want to look into monitoring tools to help you manage yours as well.