@anuv6295 - What is the configuration of Active and Idle requestors in your service package? When you are seeing this issue can you check the count of active and idle connections in your requestor pool. If your active count matches with your Max no of active requestors mentioned in the service package then you will get this issue. In this scenario you might need to increase the count in the service package rule.
I hope you have a service in the service package in which "End Requestor When Done" is checked to return the active connection to the pool.