For some 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
Event name=Server_Adaptive_Threshold_Metric:instance_efficiency__response_time_pt
Metric Group=Server_Adaptive_Threshold_Metric
Metric=Response Time Per Txn
Metric value=258.497253691275
Key Value=SYSTEM
Rule Name=DEFAULT_RULESET_FOR_ALL_TARGETS,METRIC_ALERT_INCIDENT_CREATION
Rule Owner=
Update Details:
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]).