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. 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.
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.