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If you stopped the EC2 instance, it will no longer be connectable until you start it again.
If your instance is stuck in a stopping state for a long period of time, there could be an issue and you should submit a ticket to have this looked at.
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asked 4 years ago
- AWS OFFICIALUpdated a year ago

Also note that if your instance was assigned a Public IP (not an Elastic IP) then it will receive a new Public IP when it is restarted which will require you to use a different DNS name to connect to it.