For one of the databases, ME ( Metric Extension ) is not collecting data. But for the rest databases, it is working fine.
Checking the ME ( Metric Extension ) definition and found an advanced option is not selected.
After creating a new version of this ME ( Metric Extension ) by checking this mentioned option, it works fine.
The reason is this database has frequent Warning/Critical response metric alert. like :
Event Type=Metric Alert
Metric=Response Time Per Txn
Metrics “Response Time Per Txn” is at 258.497
Incident created by rule (Name = Incident management rule set for all targets, Create incident for critical metric alerts [System generated rule]).