Yes, the cloud service provider does monitor the health of the key infrastructure they use for delivering their cloud services. But problems you may face on AWS could be unique to your EC2 instance, or your database instance. The cloud service provider SLAs are only around uptime of their service, not around performance, and will not help you diagnose problems with applications you have hosted on AWS. You may find our whitepaper on 6 myths of cloud performance monitoring to be of interest.