Any server you have running in any kind of environment where reliability is a factor should have some kind of monitoring system. Maybe DO should offer this feature like others do, but it's not out of the question to have another droplet running a heartbeat monitor. That'd be akin to them charging another $5/mo for the same service.
I would of course do that before I migrated. I did have munin running, but without alerts. The problem is that is crashed at all. My production server has been up for 668 days, and the temporary DO server didn't last 30.
On the production server, I do ping the server every five minutes, but the customer complaints always reach me before that system.
You can do what nagios does: ping more frequently, but not send an alert until several pings have failed. It guards against a packet lost to the ethers, but still picks up a failed service. Maybe ping every 30 secs, four missed pings = raise alert?
Even better than vacri's suggestion: set up load balancing so that you always have a server to fall back on if one goes down. Once you get the alert, you can fix the down server without the pressure of getting a down website back up.
I have production servers that have been up 3+ years, and others that died within 30 days. On AWS. So having a similar experience on DO wouldn't worry me unless it was every node.
