Short answer: Yes, you should expect any IaaS, PaaS, SaaS platform to have issues from time to time.
There's no bullet-proof system. Sometimes the vendor has issues with the underlying hardware that can affect your server/container. My first step if I think AWS is having a hardware/virtualization issue is stop and start the instance. This moves your instance to a different AWS server. You should rarely need to do this though.
What you can do is monitor and alert on metrics that would indicate your service/server is not responding. In your example, Network traffic (bytes in) below a certain threshold for a certain period of time could indicate an issue.
To further protect the availability of your site you can (depending on your use case) create a second (or multiple) instance and use an application or network load balancer to check host health and send traffic accordingly. (ALB/NLB).
Bottom line, you should always expect issues (whether using a cloud provider or your own hardware) and build monitors to alert when an issue may be present and take appropriate actions.
References
AWS High Availability White Paper