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The most common reason that MySQL will crash or become unavailable on a 512MB droplet is a lack of available memory. Droplets do not have swap space by default and the requirements for a LAMP stack, especially when running a control panel, can exhaust the available memory and cause services to crash.
You can check your available memory with:
free -m
If you find that you are low on memory you can try enabling a swap file on your droplet, optimize your MySQL configuration, or upgrade to a larger droplet plan.