Update: some further research, the problem seems to have been a failed attempt to tighten the cipher security settings.
The "solution" to this is described at VMWare KB74958, but it seems to require shell access:
To correct this issue, modify or restore the Ciphers line in /etc/ssh/sshd_config, or revert the file to its default parameters, as found in your running release of ESXi server.To modify the Ciphers line in /etc/ssh/sshd_config:
- Log into the ESXi server's shell. For additional instructions, see KB2004746
- Navigate to /etc/ssh
- Make a backup copy of the sshd_config file: cp sshd_config sshd_config.bak
- Open the sshd_config file with vi editor. For additional instructions, see KB1020302
- Correct the Ciphers line in sshd_config:
Ciphers aes128-ctr,aes192-ctr,aes256-ctr,aes128-cbc,aes192-cbc,aes256-cbc
- When finished, restart the SSH service: /etc/init.d/ssh restart
Alternatively, if you have another ESXi server of the same update level that is not producing errors upon connecting, you can compare its /etc/ssh/sshd_config configuration file contents with the impacted server's, and make adjustments, accordingly, or even copy the working configuration file to a shared datastore for eventual overwriting on the affected ESXi server(s).
Obviously, we do not have SSH access to get in and fix this. How can we get in instead?
I tried googling around for the "ESXi shell" (formerly Tech Support Mode) client to get in even when SSH is broken, but can't find how to access it.