SSH kex_exchange_identification error on new server

I setup a new Nanode server and I'm having an issue where sometimes my SSH connection closes.

I've seen both errors:

kex_exchange_identification: Connection closed by remote host
kex_exchange_identification: read: Connection reset by peer

I checked the syslog and sshd logs and it doesn't say anything when this happens, which has me suspect that this is not an issue with the server.

For the record, I first got these errors ~30 minutes after the server was created. All I've done so far is disable root logins, create an account, and install Docker.