With your critical applications relying on the cloud, any disruption in the availability can hurt the business. Most cloud service providers promise over 99% uptime, which means a total downtime of 3.65 days in a year, which is considered acceptable for most businesses. Since availability needs may vary for different users and your requirement for uptime can be higher.
You need to check if the vendor is keeping in place a strategy and providing the solutions required to accelerate disaster recovery. It is also important to opt for a provider that implements multiple disaster recovery policies. You can further evaluate the resiliency of the cloud environment by collecting data from neutral sources.