Why would it make you move away from DO? You'll run into it with any VPS no matter where.
Check your syslog for OOM killer on mysqld. If it's there, upgrade your droplet or use less RAM.

Thanks for your reply.

Could you provide details on: "Check your syslog for OOM killer on mysqld"

Thanks again for your help.

@mosaic - Errors are not specific to DigitalOcean and could pop up for any number of reasons on any VPS deployed to any provider and at any time if the software, MySQL in this case, is not tweaked and / or tuned properly. You could "downgrade" to shared hosting, though you would, as a result, lose the ability to customize your server and would thus be stuck with whatever configuration the shared host sets.

The specific connection error that you're referencing could be due to poor configuration (such as RAM being over-allocated), lack of configuration or problems elsewhere. To really dive deep in to the error and the configuration, MySQL Tuner should be used (as I referenced in another post of yours IIRC). It will allow you to see how much RAM could potentially be used by MySQL (note: if MySQL is configured to use more RAM than the Droplet is allocated and swap won't cover the excess, MySQL is going to crash as MySQL will use whatever it's allocated).

That said, there's not a specific one-shot variable that tells MySQL how much RAM it can use (when compared to MemCached or Redis, which has one configuration variable for RAM allocation). MySQL uses a combination of InnoDB settings as well as buffers, query cache etc to allocate RAM. If these are set too high, MySQL will naturally crash as a result of lack of RAM/Memory.

Problem solved with this code..

sudo start mysql

Regards,
Beautiful Jogja - Indonesia