I'm getting the same problem and I found the solution!
1) Go to your Dashboard and Power Off your droplet.
2) Go to Kernel tab and change your kernel to use: DigitalOcean GrubLoader v0.2
3) Go to Access tab and click Launch Console
4) You should see the console screen with some options to choose (hit Enter key if you don't see any)
5) Choose the interactive bash command option
6) Type "reboot" and wait, don't close the window
7) You'll be prompted to select from 3 options. Choose option #2 (boot kernel from GrubLoader)
Your droplet should start correctly again (at least in my case)
My droplet went down and unable to boot (always in recovery mode) after the NYC1 Hypervisor Reboots maintenance completed by DO:
Looking further into their post:
The most important information:
If your distribution is not included in the list of patched versions below, we highly recommend you move your data to a new Droplet running a version that is receiving security updates. To simplify the act of patching, we have recently updated Droplets to utilize a GrubLoader, which allows Droplets that use our in-control panel legacy system to boot into internally installed kernels. On certain legacy Droplets, this may cause issues if the kernel is not upgraded.*
My short answer above is based on the above information from DO.