This is a great question. We do not publish an SLA for our support tickets at this time. In most cases, support tickets are actually unnecessary and I would like to take the opportunity to provide an alternate perspective on how to handle these situations. The more we can make that known, the faster we can be there when you actually do need us.
In this case, for example, you are powering your droplet on and the droplet is powering itself back off (for whatever reason). Our support team will not have access to the inside of your droplet to know why, nor will they have any way to force it to override software issues occurring inside of the droplet. In this case, you will find that you are actually the most well equipped to run with this, without having to wait for our support team to respond.
Given that the droplet will not stay powered on due to an issue that is occurring inside of it's operating system, you should boot from the recovery ISO so that you can plan your next move:
From here you can use the web console and see various options. One option may be to mount the droplet's file system, drop into a shell, and review the system logs to see if you can troubleshoot the issue. Another option may simply be to treat this droplet as disposable, it's a valid technique in an environment where you can create new servers on demand, and perhaps you could use rsync to copy it's important data to another server.
I hope that this helps :)