have you talked to digitalocean yet. I am sure they can help you track down what is causing your server to crash and give you some ideas on what you can do.
Just contact your host and report this issue. I suppose your site is using some CMS and it's seems to bee either Brute force or some kind of attack in the site which might causing this. Just try to check access log of the site and see if you find the lot of acces from since IP address.
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