So, Resources are created automatically (via. XOG or SQL code)/manually?
It looks like there might be something has gone wrong and it might be hard to know without understanding how Resource Manager is assigned to Resource?
If it's random issue, definitely, you could change RM on Resource Properties page to someone else and revert it back. That should kick-off out-of-box mechanism and should correct RM Auto rights.
If there is some custom solution in place causing this issue, you could right another custom solution to check on frequency basis to restore Resource Manager Auto rights.
Right would be 'ResourceManagerMgmt'. (Id: 3710 and Name: Resource - Manager (Auto))