AWS EC2 connection timeout

Question

I have an Ubuntu 16.04 host on EC2 that becomes unreachable every time I forget to close ssh connection with exit command. Here are the things I have checked:

• Port 22 is open (obviously since this happens after an ssh connection is left open) for all IP addresses.
• I know the host is not dead since there is a website running on port 80 that still is accessible.
• Restart does not help. The only thing that works is terminating the instance and re creating.
• Screenshot of the host from EC2 shows only a login prompt and nothing else.
• Logging in with the integrated terminal in AWS also times out.
• My network firewall is not an issue as I made the ssh connection in the first place.

I suspect the ssh daemon is dying for some reason. If this is the case, what I don't understand is

1. Why is the ssh daemon dying just because of an SSH connection timeout.

2. If SSH Daemon is dead, why does it not start again after a restart.

If this is not the case, what else could be wrong?