Microservice architecture is a preferred way to build applications. Being flexible and loosely coupled, it allows to deploy code at a high pace. State, or, in other words, data is not only a commodity but crucial to any business. The high availability and accessibility of data enables companies to remain competitive. However, maintaining low latency stateful microservices, for example, performing updates, is difficult compared to stateless microservices. Making changes to a stateful microservice requires a graceful failover, which has an impact on the availability budget. The method of graceful failover is proposed to improve availability of a low latency stateful microservice when performing maintenance. By observing database connection activity and forcefully terminating idle client connections, the method allows to redirect database requests from one node to another with negligible impact on the client. Thus, the proposed method allows to keep the precious availability budget untouched while performing maintenance operations on low latency stateful microservices. A set of experiments was performed to evaluate stateful microservice availability during failover and to validate the method. The results have shown that near-zero downtime was achieved during a graceful failover.