Getting "There was a problem connecting to your instance" when trying to reconnect to an EC2 instance

The best suggestion I have is to contact our support team to see what is wrong here - it's not possible at this distance to see what the issue is.

However, my guess is that there is some process on the instance which is consuming all the resources (CPU, memory, etc.) and that is causing the instance to hang or for processes such as the SSH daemon to stop responding. Once you restart the instance, look in the logs to see what has been happening. If there isn't enough detail, you will need to enable additional logging or metric collection to see what is causing the issue. Again, just a guess.