Depending on the data set size and specific operations invoked for that data, the amount of memory required would be different. The health checks are certainly pounding RAM on any system the most, especially with larger backup chains to verify.
Have you tried to run the health check while the other jobs/activities targetting the same storage are stopped? By eliminating the other factors like contention for the resources, you'd be able to determine if the issue exists only within specific conditions or manifests itself at all times, irrespective to the load on the storage.
Product Architect @ SingleHop - Veeam Platinum Service Provider
VCAP-DCD, VCAP-DCA, VCP-NV
Veeam Certified Architect