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The key line in that log output is this:
150217 9:04:29 InnoDB: Fatal error: cannot allocate memory for the buffer pool
Your droplet did not have the available RAM for the service. Without sufficient memory available MySQL may fail to start or crash when it exhausts the physical memory. There are a few things you can do to address this issue. Please note that rebooting when this occurs is not a workable solution as frequent database crashes will likely result in your database ending up corrupted and possibly unrecoverable.
1.) You can upgrade to a larger droplet plan in order to provide more memory for the process.
2.) You can enable a swap file on your droplet. This will be used when memory is exhausted and can prevent these crashes. This tutorial will guide you in setting this up.
3.) You can work to optimize your scripts, MySQL configuration and other services to lessen the amount of memory in use.
I would recommend doing all three of these things. Just doing #2 immediately should stop the crashes while you investigate the other two options.